File "markSceme-SL-paper3.html"
Path: /IB QUESTIONBANKS/5 Fifth Edition - PAPER/HTML/Physics/Option A HTML/markSceme-SL-paper3html
File size: 1.6 MB
MIME-type: text/html
Charset: utf-8
<!DOCTYPE html>
<html>
<meta http-equiv="content-type" content="text/html;charset=utf-8">
<head>
<meta charset="utf-8">
<title>IB Questionbank</title>
<link rel="stylesheet" media="all" href="css/application-02ef852527079acf252dc4c9b2922c93db8fde2b6bff7c3c7f657634ae024ff1.css">
<link rel="stylesheet" media="print" href="css/print-6da094505524acaa25ea39a4dd5d6130a436fc43336c0bb89199951b860e98e9.css">
<script src="js/application-9717ccaf4d6f9e8b66ebc0e8784b3061d3f70414d8c920e3eeab2c58fdb8b7c9.js"></script>
<script type="text/javascript" async src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.5/MathJax.js?config=TeX-MML-AM_CHTML-full"></script>
<!--[if lt IE 9]>
<script src='https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js'></script>
<![endif]-->
<meta name="csrf-param" content="authenticity_token">
<meta name="csrf-token" content="iHF+M3VlRFlNEehLVICYgYgqiF8jIFlzjGNjIwqOK9cFH3ZNdavBJrv/YQpz8vcspoICfQcFHW8kSsHnJsBwfg==">
<link href="favicon.ico" rel="shortcut icon">
</head>
<body class="teacher questions-show">
<div class="navbar navbar-fixed-top">
<div class="navbar-inner">
<div class="container">
<div class="brand">
<div class="inner"><a href="http://ibo.org/">ibo.org</a></div>
</div>
<ul class="nav">
<li>
<a href="../../../../../../../index.html">Home</a>
</li>
<!-- - if current_user.is_language_services? && !current_user.is_publishing? -->
<!-- %li= link_to "Language services", tolk_path -->
</ul>
<ul class="nav pull-right">
<li class="dropdown">
<a class="dropdown-toggle" data-toggle="dropdown" href="#">
Help
<b class="caret"></b>
</a>
<ul class="dropdown-menu">
<li><a href="https://questionbank.ibo.org/video_tour?locale=en">Video tour</a></li>
<li><a href="https://questionbank.ibo.org/instructions?locale=en">Detailed instructions</a></li>
<li><a target="_blank" href="https://ibanswers.ibo.org/">IB Answers</a></li>
</ul>
</li>
<li>
<a href="https://06082010.xyz">IB Documents (2) Team</a>
</li></ul>
</div>
</div>
</div>
<div class="page-content container">
<div class="row">
<div class="span24">
<div class="pull-right screen_only"><a class="btn btn-small btn-info" href="https://questionbank.ibo.org/updates?locale=en">Updates to Questionbank</a></div>
<p class="muted language_chooser">
User interface language:
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=en">English</a>
|
<a href="https://questionbank.ibo.org/en/users/set_user_locale?new_locale=es">Español</a>
</p>
</div>
</div>
<div class="page-header">
<div class="row">
<div class="span16">
<p class="back-to-list">
</p>
</div>
<div class="span8" style="margin: 0 0 -19px 0;">
<img style="width: 100%;" class="qb_logo" src="https://mirror.ibdocs.top/qb.png" alt="Ib qb 46 logo">
</div>
</div>
</div>
<h2>SL Paper 3</h2><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define<em> proper length.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A charged pion decays spontaneously in a time of 26 ns as measured in the frame of reference in which it is stationary. The pion moves with a velocity of 0.96<em>c</em> relative to the Earth. Calculate the pion’s lifetime as measured by an observer on the Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the pion reference frame, the Earth moves a distance X before the pion decays. In the Earth reference frame, the pion moves a distance Y before the pion decays. Demonstrate, with calculations, how length contraction applies to this situation.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the length of an object in its rest frame</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{\sqrt {\left( {1 - {{0.96}^2}} \right)} }}">
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mrow>
<mo>(</mo>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>0.96</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</msqrt>
</mrow>
</mfrac>
</math></span> <em><strong>OR </strong></em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma = 3.6">
<mi>γ</mi>
<mo>=</mo>
<mn>3.6</mn>
</math></span><br><em>ECF for wrong </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma">
<mi>γ</mi>
</math></span></p>
<p>93 «ns»<br><em>Award <strong>[2]</strong> for a bald correct answer.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«X is» 7.5 «m» in frame on pion</p>
<p>«Y is» 26.8 «m» in frame on Earth </p>
<p>identifies proper length as the Earth measurement<br><em><strong>OR<br></strong></em>identifies Earth distance according to pion as contracted length<br><em><strong>OR<br></strong></em>a statement explaining that one of the length is shorter than the other one</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>An electron X is moving parallel to a current-carrying wire. The positive ions and the wire are fixed in the reference frame of the laboratory. The drift speed of the free electrons in the wire is the same as the speed of the external electron X.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define <em>frame of reference.</em></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>In the reference frame of the laboratory the force on X is magnetic.</p>
<p>(i) State the nature of the force acting on X in this reference frame where X is at rest.</p>
<p>(ii) Explain how this force arises.</p>
<div class="marks">[4]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a coordinate system<br><em><strong>OR<br></strong></em>a system of clocks and measures providing time and position relative to an observer</p>
<p><em>OWTTE</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>i</p>
<p>electric<br><em><strong>OR<br></strong></em>electrostatic</p>
<p> </p>
<p>ii</p>
<p>«as the positive ions are moving with respect to the charge,» there is a length contraction</p>
<p>therefore the charge density on ions is larger than on electrons</p>
<p>so net positive charge on wire attracts X</p>
<p><em>For candidates who clearly interpret the question to mean that X is now at rest in the Earth frame accept this alternative MS for bii<br>the magnetic force on a charge exists only if the charge is moving <br>an electric force on X , if stationary, only exists if it is in an electric field <br>no electric field exists in the Earth frame due to the wire <br>and look back at b i, and award mark for there is no electric or magnetic force on X</em></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>Identical twins, A and B, are initially on Earth. Twin A remains on Earth while twin B leaves the Earth at a speed of 0.6<em>c</em> for a return journey to a point three light years from Earth.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the time taken for the journey in the reference frame of twin A as measured on Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time taken for the journey in the reference frame of twin B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, for the reference frame of twin A, a spacetime diagram that represents the worldlines for both twins.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest how the twin paradox arises and how it is resolved.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>«0.6 <em>ct</em> = 6 ly» so <em>t</em> = 10 «years»</p>
<p> <em>Accept: If the 6 ly are considered to be measured from B, then the answer is 12.5 years.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>10<sup>2 </sup>− 6<sup>2 </sup>= <em>t</em><sup>2 </sup>− 0<sup>2</sup></p>
<p>so <em>t</em> is 8 «years»<em><br>Accept: If the 6 ly are considered to be measured from B, then the answer is 10 years.</em></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>gamma is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{4}">
<mfrac>
<mn>5</mn>
<mn>4</mn>
</mfrac>
</math></span></p>
<p>10 × <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{5}">
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
</math></span> = 8 «years»</p>
<p><em>Allow ECF from a<br>Allow ECF for incorrect γ in mp1<br></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>three world lines as shown</p>
<p><img src="data:image/png;base64,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"></p>
<p><em>Award mark only if axes <strong>OR</strong> world lines are labelled.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>according to both twins, it is the other one who is moving fast therefore clock should run slow</p>
<p><em>Allow explanation in terms of spacetime diagram.</em></p>
<p>«it is not considered a paradox as» twin B is not always in the same inertial frame of reference</p>
<p><em><strong>OR</strong></em></p>
<p>twin B is actually accelerating «and decelerating»</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer P sitting in a train moving at a speed <em>v</em> measures that his journey takes a time Δ<em>t</em><sub>P</sub>. An observer Q at rest with respect to the ground measures that the journey takes a time Δ<em>t</em><sub>Q</sub>.</p>
</div>
<div class="specification">
<p>According to Q there is an instant at which the train is completely within the tunnel.</p>
<p>At that instant two lights at the front and the back of the train are turned on simultaneously according to Q.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>The spacetime diagram according to observer Q shows event B (back light turns on) and event F (front light turns on).</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-26_om_14.55.20.png" alt="M17/4/PHYSI/SP3/ENG/TZ1/4d_02"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State which of the two time intervals is a proper time.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed <em>v</em> of the train for the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta {t_{\text{P}}}}}{{\Delta {t_{\text{Q}}}}} = 0.30">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
<mn>0.30</mn>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Later the train is travelling at a speed of 0.60c. Observer P measures the length of the train to be 125 m. The train enters a tunnel of length 100 m according to observer Q.</p>
<p>Show that the length of the train according to observer Q is 100 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the time <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ct'">
<mi>c</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
</math></span> and space <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x'">
<msup>
<mi>x</mi>
<mo>′</mo>
</msup>
</math></span> axes for observer P’s reference frame on the spacetime diagram.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, using the spacetime diagram, which light was turned on first according to observer P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Apply a Lorentz transformation to show that the time difference between events B and F according to observer P is 2.5 × 10<sup>–7</sup> s.</p>
<div class="marks">[1]</div>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate that the spacetime interval between events B and F is invariant.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.iv.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second train is moving at a velocity of –0.70c with respect to the ground.</p>
<p><img src="data:image/png;base64,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"></p>
<p>Calculate the speed of the second train relative to observer P.</p>
<p> </p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>Δ<em>t</em><sub>P</sub> / observer sitting in the train</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma = \frac{{\Delta {t_{\text{Q}}}}}{{\Delta {t_{\text{P}}}}} = ">
<mi>γ</mi>
<mo>=</mo>
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>Q</mtext>
</mrow>
</msub>
</mrow>
</mrow>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mrow>
<mtext>P</mtext>
</mrow>
</msub>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{1}{{0.30}}">
<mo>=</mo>
<mfrac>
<mn>1</mn>
<mrow>
<mn>0.30</mn>
</mrow>
</mfrac>
</math></span>» = 3.3</p>
<p>to give<em> v</em> = 0.95c</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span> = 1.25</p>
<p>«length of train according Q» = 125/1.25</p>
<p>«giving 100m»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>axes drawn with correct gradients of <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{3}">
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</math></span> for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ct'">
<mi>c</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
</math></span> and 0.6 for <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x'">
<msup>
<mi>x</mi>
<mo>′</mo>
</msup>
</math></span></p>
<p> </p>
<p><em>Award <strong>[1]</strong> for one gradient correct <strong>and</strong> another approximately correct.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>lines parallel to the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x'">
<msup>
<mi>x</mi>
<mo>′</mo>
</msup>
</math></span> axis and passing through B and F</p>
<p>intersections on the <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="ct'">
<mi>c</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
</math></span> axis at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{B'}}">
<mrow>
<mtext>B'</mtext>
</mrow>
</math></span> and <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\text{F'}}">
<mrow>
<mtext>F'</mtext>
</mrow>
</math></span> shown</p>
<p>light at the front of the train must have been turned on first</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta t' = 1.25 \times \frac{{0.6 \times 100}}{{3 \times {{10}^8}}}">
<mi mathvariant="normal">Δ</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>1.25</mn>
<mo>×</mo>
<mfrac>
<mrow>
<mn>0.6</mn>
<mo>×</mo>
<mn>100</mn>
</mrow>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></p>
<p>«2.5 × 10<sup>−7</sup>»</p>
<p> </p>
<p><em>Allow ECF for gamma from (c).</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>according to P: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {3 \times {{10}^8} \times 2.5 \times {{10}^{ - 7}}} \right)^2} - {125^2} = ">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>2.5</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>7</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mn>125</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
</math></span> «−» 10000</p>
<p>according to Q: <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="{\left( {3 \times {{10}^8} \times 0} \right)^2} - {100^2} = ">
<mrow>
<msup>
<mrow>
<mo>(</mo>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
<mo>×</mo>
<mn>0</mn>
</mrow>
<mo>)</mo>
</mrow>
<mn>2</mn>
</msup>
</mrow>
<mo>−</mo>
<mrow>
<msup>
<mn>100</mn>
<mn>2</mn>
</msup>
</mrow>
<mo>=</mo>
</math></span> «−» 10000</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="u' = \frac{{ - 0.7 - 0.6}}{{1 + 0.7 \times 0.6}}">
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>0.7</mn>
<mo>−</mo>
<mn>0.6</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>0.7</mn>
<mo>×</mo>
<mn>0.6</mn>
</mrow>
</mfrac>
</math></span> <strong>c</strong></p>
<p>= «−» 0.92c</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.iv.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State <strong>one</strong> prediction of Maxwell’s theory of electromagnetism that is consistent with special relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A current is established in a long straight wire that is at rest in a laboratory.</p>
<p><img src="data:image/png;base64,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"></p>
<p>A proton is at rest relative to the laboratory and the wire.</p>
<p>Observer X is at rest in the laboratory. Observer Y moves to the right with constant speed relative to the laboratory. Compare and contrast how observer X and observer Y account for any non-gravitational forces on the proton.</p>
<p> </p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the speed of light is a universal constant/invariant<br><em><strong>OR</strong></em><br><em>c</em> does not depend on velocity of source/observer</p>
<p>electric and magnetic fields/forces unified/frame of reference dependant</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>observer X will measure zero «magnetic or electric» force</p>
<p>observer Y must measure both electric and magnetic forces</p>
<p>which must be equal and opposite so that observer Y also measures zero force</p>
<p> </p>
<p><em>Allow <strong>[2 max]</strong> for a comment that both X and Y measure zero resultant force even if no valid explanation is given.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket of proper length 450 m is approaching a space station whose proper length is 9.0 km. The speed of the rocket relative to the space station is 0.80<em>c</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>X is an observer at rest in the space station.</p>
<p> </p>
</div>
<div class="specification">
<p>Two lamps at opposite ends of the space station turn on at the same time according to X. Using a Lorentz transformation, determine, according to an observer at rest in the rocket,</p>
</div>
<div class="specification">
<p>The rocket carries a different lamp. Event 1 is the flash of the rocket’s lamp occurring at the origin of <strong>both</strong> reference frames. Event 2 is the flash of the rocket’s lamp at time<em> ct'</em> = 1.0 m according to the rocket. The coordinates for event 2 for observers in the space station are <em>x</em> and <em>ct</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2017-09-27_om_07.57.21.png" alt="M17/4/PHYSI/SP3/ENG/TZ2/05c"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the length of the rocket according to X.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A space shuttle is released from the rocket. The shuttle moves with speed 0.20<em>c</em> <strong>to the right</strong> according to X. Calculate the <strong>velocity</strong> of the shuttle relative to the rocket.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>the time interval between the lamps turning on.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>which lamp turns on first.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>On the diagram label the coordinates <em>x</em> and <em>ct</em>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the <em>ct</em> coordinate in (c)(i) is less than, equal to <strong>or </strong>greater than 1.0 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the value of <em>c</em> <sup>2</sup><em>t </em><sup>2</sup> – <em>x </em><sup>2</sup>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the gamma factor is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{3}">
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</math></span> <em><strong>or</strong></em> 1.67</p>
<p><em>L</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{450}}{{\frac{5}{3}}}">
<mfrac>
<mrow>
<mn>450</mn>
</mrow>
<mrow>
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
</mrow>
</mfrac>
</math></span> = 270 «m»</p>
<p> </p>
<p><em>Allow ECF from MP1 to MP2.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>u'</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}} = ">
<mfrac>
<mrow>
<mi>u</mi>
<mo>−</mo>
<mi>v</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mi>u</mi>
<mi>v</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.20c - 0.80c}}{{1 - 0.20 \times 0.80}}">
<mfrac>
<mrow>
<mn>0.20</mn>
<mi>c</mi>
<mo>−</mo>
<mn>0.80</mn>
<mi>c</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mn>0.20</mn>
<mo>×</mo>
<mn>0.80</mn>
</mrow>
</mfrac>
</math></span><br><em><strong>OR<br></strong></em>0.2<em>c = </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" = \frac{{0.80c + u'}}{{1 + 0.80u'}}">
<mo>=</mo>
<mfrac>
<mrow>
<mn>0.80</mn>
<mi>c</mi>
<mo>+</mo>
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>0.80</mn>
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
</mrow>
</mfrac>
</math></span></p>
<p><em>u'</em> = «–»0.71<em>c</em></p>
<p> </p>
<p><em>Check signs and values carefully.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>Δt'</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma \left( {\Delta t - \frac{{v\Delta x}}{{{c^2}}}} \right) = ">
<mi>γ</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mi mathvariant="normal">Δ</mi>
<mi>x</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
</math></span>» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{5}{3} \times \left( {0 - \frac{{\left( {0.80c \times 9000} \right)}}{{{c^2}}}} \right)">
<mfrac>
<mn>5</mn>
<mn>3</mn>
</mfrac>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.80</mn>
<mi>c</mi>
<mo>×</mo>
<mn>9000</mn>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em>Δt' = </em>«–»4.0 x 10<sup>–5</sup> «s»</p>
<p> </p>
<p><em>Allow ECF for use of wrong <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span> from (a)(i).</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>lamp 2 turns on first</p>
<p><em>Ignore any explanation</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>x</em> coordinate as shown</p>
<p><em>ct</em> coordinate as shown</p>
<p><img src="data:image/png;base64,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"></p>
<p> </p>
<p><em>Labels must be clear and unambiguous.</em></p>
<p><em>Construction lines are optional.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>«in any other frame» <em>ct</em> is greater</p>
<p>the interval <em>ct'</em> = 1.0 «m» is proper time<br><em><strong>OR</strong></em><br><em>ct</em> is a dilated time<br><em><strong>OR</strong></em><br><em>ct</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span><em>ct'</em> «= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span>»</p>
<p> </p>
<p><em>MP1 is a statement</em></p>
<p><em>MP2 is an explanation</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of <em>c</em> <sup>2</sup><em>t </em><sup>2</sup> – <em>x </em><sup>2<em> </em></sup>= <em>c</em> <sup>2</sup><em>t' </em><sup>2</sup> – <em>x'</em> <sup>2</sup><br><br><em>c</em> <sup>2</sup><em>t </em><sup>2</sup> – <em>x </em><sup>2<em> </em></sup>= 1<sup>2</sup> – 0<sup>2 </sup>= 1 «m<sup>2</sup>»</p>
<p> </p>
<p><em>for MP1 equation must be used.</em></p>
<p><em>Award <strong>[2]</strong> for correct answer that first finds x (1.33 m) and ct (1.66 m)</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.iii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.iii.</div>
</div>
<br><hr><br><div class="question">
<p>Muons are unstable particles with a proper lifetime of 2.2 μs. Muons are produced 2.0 km above ground and move downwards at a speed of 0.98<em>c</em> relative to the ground. For this speed <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span> = 5.0. Discuss, with suitable calculations, how this experiment provides evidence for time dilation.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p><em><strong>ALTERNATIVE 1</strong> — for answers in terms of time</em><br>overall idea that more muons are detected at the ground than expected «without time dilation»</p>
<p>«Earth frame transit time = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2000}}{{0.98c}}">
<mfrac>
<mrow>
<mn>2000</mn>
</mrow>
<mrow>
<mn>0.98</mn>
<mi>c</mi>
</mrow>
</mfrac>
</math></span>» = 6.8 «μs»</p>
<p>«Earth frame dilation of proper half-life = 2.2 μs x 5» = 11 «μs»<br><em><strong>OR</strong></em><br>«muon’s proper transit time = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{6.8\mu s}}{5}">
<mfrac>
<mrow>
<mn>6.8</mn>
<mi>μ</mi>
<mi>s</mi>
</mrow>
<mn>5</mn>
</mfrac>
</math></span>» = 1.4 «μs»</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2</strong></em> <em>– for answers in terms of distance</em><br>overall idea that more muons are detected at the ground than expected «without time dilation»</p>
<p>«distance muons can travel in a proper lifetime = 2.2 μs x 0.98<em>c</em>» = 650 «m»</p>
<p>«Earth frame lifetime distance due to time dilation = 650 m x 5» = 3250 «m»<br><em><strong>OR</strong></em><br>«muon frame distance travelled = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2000}}{5}">
<mfrac>
<mrow>
<mn>2000</mn>
</mrow>
<mn>5</mn>
</mfrac>
</math></span>» = 400 «m»</p>
<p> </p>
<p><em>Accept answers from <strong>one</strong> of the alternatives.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br><div class="specification">
<p>A spaceship S leaves the Earth with a speed <em>v </em>= 0.80<em>c</em>. The spacetime diagram for the Earth is shown. A clock on the Earth and a clock on the spaceship are synchronized at the origin of the spacetime diagram.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the angle between the worldline of S and the worldline of the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw, on the diagram, the <em>x′</em>-axis for the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An event Z is shown on the diagram. Label the co-ordinates of this event in the reference frame of S.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>angle = tan<sup>–1 </sup>«<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.8}}{1}">
<mfrac>
<mrow>
<mn>0.8</mn>
</mrow>
<mn>1</mn>
</mfrac>
</math></span>» = 39 «<sup>o</sup>» <em><strong>OR</strong></em> 0.67 «rad»</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>adds <em>x</em>′-axis as shown</p>
<p><img src="data:image/png;base64,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"></p>
<p><em>Approximate same angle to v = c as for ct′. </em></p>
<p><em>Ignore labelling of that axis.</em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>adds two lines parallel to <em>ct</em>′ and <em>x</em>′ as shown indicating coordinates</p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A long current-carrying wire is at rest in the reference frame S of the laboratory. A positively charged particle P outside the wire moves with velocity <em>v</em> relative to S. The electrons making up the current in the wire move with the same velocity<em> v</em> relative to S.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a reference frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in reference frame S.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State and explain whether the force experienced by P is magnetic, electric or both, in the rest frame of P.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a set of coordinate axes and clocks used to measure the position «in space/time of an object at a particular time»<br><em><strong>OR</strong></em><br>a coordinate system to measure x,y,z, and t / OWTTE</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>magnetic only</p>
<p>there is a current but no «net» charge «in the wire»</p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>electric only</p>
<p>P is <strong>stationary</strong> so experiences no magnetic force</p>
<p>relativistic contraction will increase the density of protons in the wire</p>
<p><em><strong>[3 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Two parallel current-carrying wires have equal currents in the same direction. There is an attractive force between the wires.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Maxwell’s equations led to the constancy of the speed of light. Identify what Maxwell’s equations describe.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State a postulate that is the same for both special relativity and Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the nature of the attractive force recorded by an observer stationary with respect to the wires.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>A second observer moves at the drift velocity of the electron current in the wires. Discuss how this observer accounts for the force between the wires.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">mention of electric </span><em><span class="fontstyle2"><strong>AND</strong> </span></em><span class="fontstyle0">magnetic fields </span><span class="fontstyle3">✓<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">mention of electromagnetic radiation/wave/fields </span><span class="fontstyle3">✓</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">the laws of physics are the same in all «inertial» frames of reference/for all «inertial» observers </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle3">OWTTE</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">magnetic </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">«In observer frame» protons «in the two wires» move in same/parallel direction </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">these moving protons produce magnetic attraction </span><span class="fontstyle2">✓</span></p>
<p><span class="fontstyle0">there is also a smaller electrostatic repulsion due to wires appearing positive due to length contraction «of proton spacing» </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle3">OWTTE</span></em></p>
<div class="question_part_label">c(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Easy introduction fairly well answered by most candidates.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>With a few exceptions referring to Newton's first, this was very well answered.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most scored by recognizing the force as magnetic.</p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many failed to recognize that the magnetic force would still be present due to the current produced by the relative motion of the protons in both wires, and only focused on the repulsive electrostatic due to length contraction.</p>
<div class="question_part_label">c(ii).</div>
</div>
<br><hr><br><div class="specification">
<p>A spaceship is travelling at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>80</mn><mi>c</mi></math>, away from Earth. It launches a probe away from Earth, at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>50</mn><mi>c</mi></math> relative to the spaceship. An observer on the probe measures the length of the probe to be <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>0</mn><mo> </mo><mi mathvariant="normal">m</mi></math>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The Lorentz transformations assume that the speed of light is constant. Outline what the Galilean transformations assume.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce the length of the probe as measured by an observer in the spaceship.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain which of the lengths is the proper length.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the probe in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math>, relative to Earth.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">constancy of time<br></span><span class="fontstyle2"><em><strong>OR</strong></em><br></span><span class="fontstyle0">speed of light > c is possible </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><em><span class="fontstyle4">OWTTE</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>15</mn></math> <span class="fontstyle3">✓<br></span></p>
<p><span class="fontstyle2">length = <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>6</mn><mo>.</mo><mn>9</mn><mo> </mo><mo>«</mo><mi mathvariant="normal">m</mi><mo>»</mo></math> </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><em><span class="fontstyle4">Allow length in the range <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">6</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">7</mn></math> to <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">7</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">0</mn><mo> </mo><mi>m</mi></math>.</span></em></p>
<p><em><span class="fontstyle4">Allow ECF from wrong </span><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi></math></span></em></p>
<p><em><span class="fontstyle4">Award </span><strong><span class="fontstyle5">[2] </span></strong><span class="fontstyle4">marks for a bald correct answer in the range indicated above.</span></em></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>8</mn><mo>.</mo><mn>0</mn><mo> </mo><mi mathvariant="normal">m</mi></math> / measurement made on the probe </span><span class="fontstyle2">✓<br></span></p>
<p><span class="fontstyle0">the measurement made by an observer at rest in the frame of the probe </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mi>c</mi><mo>+</mo><mn>0</mn><mo>.</mo><mn>8</mn><mi>c</mi></mrow><mrow><mn>1</mn><mo>+</mo><mstyle displaystyle="true"><mfrac><mrow><mn>0</mn><mo>.</mo><mn>5</mn><mi>c</mi><mo>×</mo><mn>0</mn><mo>.</mo><mn>8</mn><mi>c</mi></mrow><msup><mi>c</mi><mn>2</mn></msup></mfrac></mstyle></mrow></mfrac></math> </span><span class="fontstyle2">✓<br></span></p>
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>=</mo><mn>0</mn><mo>.</mo><mn>93</mn><mtext>c</mtext></math> </span><span class="fontstyle2">✓</span></p>
<p> </p>
<p><em><span class="fontstyle2">Allow <strong>all</strong> negative signs for velocities<br></span></em></p>
<p><em><span class="fontstyle2">Award <strong>[2]</strong> marks for a bald correct answer</span></em></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Although the expected answers was the constancy of time, the markscheme allowed references to the speed of light not being constant, as this was a common answer, deriving from the stem used in the question.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very well answered.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>"In the same frame" does not highlight the need to be "at rest" in that frame, and was the most frequent wrong answer, although a vast majority scored full marks here.</p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Very well answered.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>Two rockets, A and B, are moving towards each other on the same path. From the frame of reference of the Earth, an observer measures the speed of A to be 0.6<em>c</em> and the speed of B to be 0.4<em>c</em>. According to the observer on Earth, the distance between A and B is 6.0 x 10<sup>8</sup> m.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Define frame of reference.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the observer on Earth, the time taken for A and B to meet.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Identify the terms in the formula.</p>
<p><em>u′</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{u - v}}{{1 - \frac{{uv}}{{{c^2}}}}}">
<mfrac>
<mrow>
<mi>u</mi>
<mo>−</mo>
<mi>v</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mi>u</mi>
<mi>v</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
</math></span></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the velocity of B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, according to an observer in A, the time taken for B to meet A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, without further calculation, how the time taken for A to meet B, according to an observer in B, compares with the time taken for the same event according to an observer in A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a co-ordinate system in which measurements «of distance and time» can be made</p>
<p><em>Ignore any mention to inertial reference frame.</em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>closing speed = <em>c</em></p>
<p>2 «s»</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>u</em> and <em>v</em> are velocities with respect to the same frame of reference/Earth <em><strong>AND</strong> u′</em> the relative velocity</p>
<p><em>Accept 0.4c and 0.6c for u and v</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ - 0.4 - 0.6}}{{1 + 0.24}}">
<mfrac>
<mrow>
<mo>−</mo>
<mn>0.4</mn>
<mo>−</mo>
<mn>0.6</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>0.24</mn>
</mrow>
</mfrac>
</math></span></p>
<p>«–» 0.81<em>c</em></p>
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma ">
<mi>γ</mi>
</math></span> = 1.25</p>
<p>so the time is <em>t </em>= 1.6 «s»</p>
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>gamma is smaller for B</p>
<p>so time is greater than for A</p>
<div class="question_part_label">e.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">e.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Muons are created in the upper atmosphere of the Earth at an altitude of 10 km above the surface. The muons travel vertically down at a speed of 0.995<em>c </em>with respect to the Earth. When measured at rest the average lifetime of the muons is 2.1 μs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to Galilean relativity, the time taken for a muon to travel to the ground.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce why only a small fraction of the total number of muons created is expected to be detected at ground level according to Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, according to the theory of special relativity, the time taken for a muon to reach the ground in the reference frame of the muon.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss how your result in (b)(i) and the outcome of the muon decay experiment support the theory of special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{{{10}^4}}}{{0.995 \times 3 \times {{10}^8}}} = ">
<mfrac>
<mrow>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>4</mn>
</msup>
</mrow>
</mrow>
<mrow>
<mn>0.995</mn>
<mo>×</mo>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
<mo>=</mo>
</math></span><strong>»</strong> 34 <strong>«</strong><em>μ</em>s<strong>»</strong></p>
<p> </p>
<p><em>Do not accept 10</em><sup><em>4</em></sup><em>/c = 33 μ</em><em>s</em><em>.</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>time is much longer than 10 times the average life time <strong>«</strong>so only a small proportion would not decay<strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma = 10">
<mi>γ</mi>
<mo>=</mo>
<mn>10</mn>
</math></span></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta {t_0} = ">
<mi mathvariant="normal">Δ</mi>
<mrow>
<msub>
<mi>t</mi>
<mn>0</mn>
</msub>
</mrow>
<mo>=</mo>
</math></span> <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\Delta t}}{\gamma } = \frac{{34}}{{10}} = ">
<mfrac>
<mrow>
<mi mathvariant="normal">Δ</mi>
<mi>t</mi>
</mrow>
<mi>γ</mi>
</mfrac>
<mo>=</mo>
<mfrac>
<mrow>
<mn>34</mn>
</mrow>
<mrow>
<mn>10</mn>
</mrow>
</mfrac>
<mo>=</mo>
</math></span><strong>»</strong> 3.4<strong> «</strong><em>μs</em><strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the value found in (b)(i) is of similar magnitude to average life time</p>
<p>significant number of muons are observed on the ground</p>
<p><strong>«</strong>therefore this supports the special theory<strong>»</strong></p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>An observer on Earth watches rocket A travel away from Earth at a speed of 0.80<em>c</em>. The spacetime diagram shows the worldline of rocket A in the frame of reference of the Earth observer who is at rest at <em>x </em>= 0.</p>
<p style="text-align: left;"><img src="data:image/png;base64,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"></p>
<p>Another rocket, B, departs from the same location as A but later than A at <em>ct </em>= 1.2 km according to the Earth observer. Rocket B travels at a constant speed of 0.60<em>c </em>in the opposite direction to A according to the Earth observer.</p>
</div>
<div class="specification">
<p>Rocket A and rocket B both emit a flash of light that are received simultaneously by the Earth observer. Rocket A emits the flash of light at a time coordinate <em>ct </em>= 1.8 km according to the Earth observer.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw on the spacetime diagram the worldline of B according to the Earth observer and label it B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce, showing your working on the spacetime diagram, the value of <em>ct </em>according to the Earth observer at which the rocket B emitted its flash of light.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain whether or not the arrival times of the two flashes in the Earth frame are simultaneous events in the frame of rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of rocket B relative to rocket A.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>straight line with negative gradient with vertical intercept at <em>ct</em> = 1.2 «km»</p>
<p>through (–0.6, 2.2) <em>ie </em>gradient = –1.67</p>
<p><img src="images/Schermafbeelding_2018-08-11_om_10.02.40.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/05.a/M"></p>
<p> </p>
<p><em>Tolerance: Allow gradient from interval –2.0 to –1.4, (at ct =</em> <em>2.2, x from interval 0.5 to 0.7).</em></p>
<p><em>If line has positive gradient from interval 1.4 to 2.0 and intercepts at ct =</em> <em>1.2 km then allow </em><strong><em>[1 max]</em></strong><em>.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line for the flash of light from A correctly drawn</p>
<p>line for the flash of light of B correctly drawn</p>
<p>correct reading taken for time of intersection of flash of light and path of B, <em>ct =</em> 2.4 <strong>«</strong>km<strong>»</strong></p>
<p><img src="images/Schermafbeelding_2018-08-11_om_10.10.53.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/05.b/M"></p>
<p> </p>
<p><em>Accept values in the range: 2.2 to 2.6.</em></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>the two events take place in the same point in space at the same time</p>
<p>so all observers will observe the two events to be simultaneous / so zero difference</p>
<p> </p>
<p><em>Award the second MP only if the first MP is awarded.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="u' = \frac{{ - 0.6 - 0.8}}{{1 - ( - 0.6) \times 0.8}}">
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>0.6</mn>
<mo>−</mo>
<mn>0.8</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.6</mn>
<mo stretchy="false">)</mo>
<mo>×</mo>
<mn>0.8</mn>
</mrow>
</mfrac>
</math></span></p>
<p>= <strong>«</strong>–<strong>»</strong>0.95<strong> «</strong><em>c</em><strong>»</strong></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>Observer A detects the creation (event 1) and decay (event 2) of a nuclear particle. After creation, the particle moves at a constant speed relative to A. As measured by A, the distance between the events is 15 m and the time between the events is 9.0 × 10<sup>–8</sup> s.</p>
<p>Observer B moves with the particle.</p>
<p>For event 1 and event 2,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by the statement that the spacetime interval is an invariant quantity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>calculate the spacetime interval.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>determine the time between them according to observer B.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline why the observed times are different for A and B.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>quantity that is the same/constant in all inertial frames</p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>spacetime interval = 27<sup>2</sup> – 15<sup>2</sup> = 504 <strong>«</strong>m<sup>2</sup><strong>»</strong></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>Evidence of <em>x</em>′ = 0</p>
<p><em>t</em>′ <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\sqrt {504} }}{c}">
<mfrac>
<mrow>
<msqrt>
<mn>504</mn>
</msqrt>
</mrow>
<mi>c</mi>
</mfrac>
</math></span><strong>»</strong> = 7.5 × 10<sup>–8</sup> <strong>«</strong>s<strong>»</strong></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><em>γ</em> = 1.2</p>
<p><em>t</em>′ <strong>«</strong>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{9 \times {{10}^{ - 8}}}}{{1.2}}">
<mfrac>
<mrow>
<mn>9</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>8</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>1.2</mn>
</mrow>
</mfrac>
</math></span><strong>»</strong> = 7.5 × 10<sup>–8</sup> <strong>«</strong>s<strong>»</strong></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>observer B measures the proper time and this is the shortest time measured</p>
<p><strong><em>OR</em></strong></p>
<p>time dilation occurs <strong>«</strong>for B's journey<strong>» </strong>according to A</p>
<p><strong><em>OR</em></strong></p>
<p>observer B is stationary relative to the particle, observer A is not</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>A train is passing through a tunnel of proper length 80 m. The proper length of the train is 100 m. According to an observer at rest relative to the tunnel, when the front of the train coincides with one end of the tunnel, the rear of the train coincides with the other end of the tunnel.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Explain what is meant by proper length.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw a spacetime diagram for this situation according to an observer at rest relative to the tunnel.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the train, according to an observer at rest relative to the tunnel, at which the train fits the tunnel.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>For an observer on the train, it is the tunnel that is moving and therefore will appear length contracted. This seems to contradict the observation made by the observer at rest to the tunnel, creating a paradox. Explain how this paradox is resolved. You may refer to your spacetime diagram in (b).</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>the length of an object in its rest frame</p>
<p><em><strong>OR</strong></em></p>
<p>the length of an object measured when at rest relative to the observer</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>world lines for front and back of tunnel parallel to <em>ct</em> axis</p>
<p>world lines for front and back of train</p>
<p>which are parallel to <em>ct′</em> axis</p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>realizes that gamma = 1.25</p>
<p>0.6<em>c</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p>indicates the two simultaneous events for <em>t</em> frame</p>
<p>marks on the diagram the different times «for both spacetime points» on the <em>ct′</em> axis «shown as Δ<em>t′</em> on each diagram»</p>
<p><img src="data:image/png;base64,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"></p>
<p><em><strong>ALTERNATIVE 2: (no diagram reference)</strong></em></p>
<p>the two events occur at different points in space</p>
<p>statement that the two events are not simultaneous in the <em>t′</em> frame</p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the axes for two inertial reference frames. Frame S represents the ground and frame S′ is a box that moves to the right relative to S with speed <em>v</em>.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>When the origins of the two frames coincide all clocks show zero. At that instant a beam of light of speed <em>c</em> is emitted from the left wall of the box towards the right wall. The box has proper length <em>L</em>. Consider the event E = light arrives at the right wall of the box.</p>
<p><br>Using <strong>Galilean</strong> relativity,</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State what is meant by a reference frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>explain why the time coordinate of E in frame S is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \frac{L}{c}">
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mi>L</mi>
<mi>c</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>hence show that the space coordinate of E in frame S is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x = L + \frac{{vL}}{c}">
<mi>x</mi>
<mo>=</mo>
<mi>L</mi>
<mo>+</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mi>L</mi>
</mrow>
<mi>c</mi>
</mfrac>
</math></span>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>a set of rulers and clocks / set of coordinates to record the position and time of events ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1:</strong></em></p>
<p>the time in frame S′ is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t' = \frac{L}{c}">
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mi>L</mi>
<mi>c</mi>
</mfrac>
</math></span> ✔</p>
<p>but time is absolute in Galilean relativity so is the same in S ✔</p>
<p> </p>
<p><em><strong>ALTERNATIVE 2:</strong></em></p>
<p>In frame S, light rays travel at <em>c</em> + <em>v</em> ✔</p>
<p><strong>so</strong> <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="t = \frac{L}{{\left( {c + v} \right) - v}} = \frac{L}{c}">
<mi>t</mi>
<mo>=</mo>
<mfrac>
<mi>L</mi>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mi>c</mi>
<mo>+</mo>
<mi>v</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>−</mo>
<mi>v</mi>
</mrow>
</mfrac>
<mo>=</mo>
<mfrac>
<mi>L</mi>
<mi>c</mi>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p><em>In Alternative 1, they must refer to S'</em></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>x</em> = <em>x</em>' + <em>vt</em> and <em>x</em>' = <em>L</em> ✔</p>
<p>«substitution to get answer»</p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket of proper length 120 m moves to the right with speed 0.82<em>c</em> relative to the ground.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p>A probe is released from the back of the rocket at speed 0.40<em>c</em> relative to the rocket.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the speed of the probe relative to the ground.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time it takes the probe to reach the front of the rocket according to an observer at rest in the rocket.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time it takes the probe to reach the front of the rocket according to an observer at rest on the ground.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{0.82c + 0.40c}}{{1 + \frac{{0.82c \times 0.40c}}{{{c^2}}}}}">
<mfrac>
<mrow>
<mn>0.82</mn>
<mi>c</mi>
<mo>+</mo>
<mn>0.40</mn>
<mi>c</mi>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mfrac>
<mrow>
<mn>0.82</mn>
<mi>c</mi>
<mo>×</mo>
<mn>0.40</mn>
<mi>c</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
</mfrac>
</math></span> ✔</p>
<p>0.92<em>c</em> ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta t' = \frac{{120}}{{0.40c}}">
<mi mathvariant="normal">Δ</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mn>120</mn>
</mrow>
<mrow>
<mn>0.40</mn>
<mi>c</mi>
</mrow>
</mfrac>
</math></span> ✔</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\Delta t' = 1.0 \times {10^{ - 6}}">
<mi mathvariant="normal">Δ</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mn>1.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mn>10</mn>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</math></span> «s» ✔</p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma = ">
<mi>γ</mi>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{\sqrt {1 - {{0.82}^2}} }} = ">
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>0.82</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 1.747 ✔</p>
<p> </p>
<p>Δ<em>t</em> = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma \left( {\Delta t' + \frac{{v\Delta x'}}{{{c^2}}}} \right)">
<mi>γ</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi mathvariant="normal">Δ</mi>
<msup>
<mi>t</mi>
<mo>′</mo>
</msup>
<mo>+</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mi mathvariant="normal">Δ</mi>
<msup>
<mi>x</mi>
<mo>′</mo>
</msup>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span>» = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.747 \times \left( {1.0 \times {{10}^{ - 6}} + \frac{{0.82c \times 120}}{{{c^2}}}} \right)">
<mn>1.747</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>1.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
<mo>+</mo>
<mfrac>
<mrow>
<mn>0.82</mn>
<mi>c</mi>
<mo>×</mo>
<mn>120</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>Δ<em>t</em> = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{120}}{{1.747 \times \left( {0.92 - 0.82} \right)c}}">
<mfrac>
<mrow>
<mn>120</mn>
</mrow>
<mrow>
<mn>1.747</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>0.92</mn>
<mo>−</mo>
<mn>0.82</mn>
</mrow>
<mo>)</mo>
</mrow>
<mi>c</mi>
</mrow>
</mfrac>
</math></span> ✔</p>
<p> </p>
<p>2.3 × 10<sup>−6</sup> «s» ✔</p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The spacetime diagram shows the axes of an inertial reference frame S and the axes of a second inertial reference frame S′ that moves relative to S with speed 0.745<em>c</em>. When clocks in both frames show zero the origins of the two frames coincide.</p>
<p><img src="data:image/png;base64,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"></p>
</div>
<div class="specification">
<p>Event E has coordinates <em>x</em> = 1 m and <em>ct</em> = 0 in frame S. Show that in frame S′ the space coordinate and time coordinate of event E are</p>
</div>
<div class="specification">
<p>A rod at rest in frame S has proper length 1.0 m. At <em>t</em> = 0 the left-hand end of the rod is at <em>x</em> = 0 and the right-hand end is at <em>x</em> = 1.0 m.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><em>x</em>′ = 1.5 m.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><em>ct</em>′ = –1.1 m.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label, on the diagram, the space coordinate of event E in the S′ frame. Label this event with the letter P.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Label, on the diagram, the event that has coordinates <em>x</em>′ = 1.0 m and <em>ct</em>′ = 0. Label this event with the letter Q.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, outline without calculation, why observers in frame S′ measure the length of the<br>rod to be less than 1.0 m.</p>
<div class="marks">[3]</div>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, estimate, in m, the length of this rod in the S′ frame.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma = ">
<mi>γ</mi>
<mo>=</mo>
</math></span> «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{\sqrt {1 - {{0.745}^2}} }} = ">
<mfrac>
<mn>1</mn>
<mrow>
<msqrt>
<mn>1</mn>
<mo>−</mo>
<mrow>
<msup>
<mrow>
<mn>0.745</mn>
</mrow>
<mn>2</mn>
</msup>
</mrow>
</msqrt>
</mrow>
</mfrac>
<mo>=</mo>
</math></span>» 1.499 ✔</p>
<p><em>x</em>′ = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma \left( {x - vt} \right) = ">
<mi>γ</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>x</mi>
<mo>−</mo>
<mi>v</mi>
<mi>t</mi>
</mrow>
<mo>)</mo>
</mrow>
<mo>=</mo>
</math></span>» 1.499 × (1.0 − 0) ✔</p>
<p>«<em>x</em>′ = 1.5 m»</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>t</em>′ = «<span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\gamma \left( {t - \frac{{vx}}{{{c^2}}}} \right)">
<mi>γ</mi>
<mrow>
<mo>(</mo>
<mrow>
<mi>t</mi>
<mo>−</mo>
<mfrac>
<mrow>
<mi>v</mi>
<mi>x</mi>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> =» <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="1.499 \times \left( {0 - \frac{{0.745c \times 1}}{{{c^2}}}} \right)">
<mn>1.499</mn>
<mo>×</mo>
<mrow>
<mo>(</mo>
<mrow>
<mn>0</mn>
<mo>−</mo>
<mfrac>
<mrow>
<mn>0.745</mn>
<mi>c</mi>
<mo>×</mo>
<mn>1</mn>
</mrow>
<mrow>
<mrow>
<msup>
<mi>c</mi>
<mn>2</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</math></span> «= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext=" - \frac{{1.11}}{c}">
<mo>−</mo>
<mfrac>
<mrow>
<mn>1.11</mn>
</mrow>
<mi>c</mi>
</mfrac>
</math></span>»</p>
<p>«<em>ct</em>′ = –1.1 m»</p>
<p><em><strong>OR</strong></em></p>
<p>using spacetime interval 0 − 1<sup>2</sup> = (<em>ct</em>′)<sup>2</sup> − 1.5<sup>2</sup> ⇒ «<em>ct</em>′ = –1.1» ✔</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line through event E parallel to <em>ct</em>′ axis meeting <em>x'</em> axis and labelled P ✔</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>point on <em>x'</em> axis about <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{2}{3}">
<mfrac>
<mn>2</mn>
<mn>3</mn>
</mfrac>
</math></span> of the way to P labelled Q ✔</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>ends of rod must be recorded at the same time in frame S′ ✔</p>
<p>any vertical line from E crossing x’, no label required ✔</p>
<p>right-hand end of rod intersects at R «whose co-ordinate is less than 1.0 m» ✔</p>
<p> </p>
<p><img src="data:image/png;base64,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"></p>
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>0.7 m ✔</p>
<div class="question_part_label">c.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows the motion of the electrons in a metal wire carrying an electric current as seen by an observer X at rest with respect to the wire. The distance between adjacent positive charges is <em>d</em>.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-11_om_06.22.52.png" alt="M18/4/PHYSI/SP3/ENG/TZ1/03"></p>
</div>
<div class="specification">
<p>Observer Y is at rest with respect to the electrons.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State whether the field around the wire according to observer X is electric, magnetic or a combination of both.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Discuss the change in <em>d </em>according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Deduce whether the overall field around the wire is electric, magnetic or a combination of both according to observer Y.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>magnetic field</p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>«</strong>according to Y<strong>» </strong>the positive charges are moving <strong>«</strong>to the right<strong>»</strong></p>
<p><em>d decreases</em></p>
<p> </p>
<p><em>For MP1, movement of positive charges must be mentioned explicitly.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>positive charges are moving, so there is a magnetic field</p>
<p>the density of positive charges is higher than that of negative charges, so there is an electric field</p>
<p> </p>
<p><em>The reason must be given for each point to be awarded.</em></p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">b.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.ii.</div>
</div>
<br><hr><br><div class="specification">
<p>Rocket A and rocket B are travelling in opposite directions from the Earth along the same straight line.</p>
<p style="text-align: center;"><img src="images/Schermafbeelding_2018-08-12_om_16.33.49.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/03"></p>
<p>In the reference frame of the Earth, the speed of rocket A is 0.75<em>c </em>and the speed of rocket B is 0.50<em>c</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Galilean transformation.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate, for the reference frame of rocket A, the speed of rocket B according to the Lorentz transformation.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Outline, with reference to special relativity, which of your calculations in (a) is more likely to be valid.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>1.25<em>c</em></p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="u' = \frac{{(0.50 + 0.75)}}{{1 + 0.5 \times 0.75}}c">
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mo stretchy="false">(</mo>
<mn>0.50</mn>
<mo>+</mo>
<mn>0.75</mn>
<mo stretchy="false">)</mo>
</mrow>
<mrow>
<mn>1</mn>
<mo>+</mo>
<mn>0.5</mn>
<mo>×</mo>
<mn>0.75</mn>
</mrow>
</mfrac>
<mi>c</mi>
</math></span></p>
<p>0.91<em>c</em></p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="u' = \frac{{ - 0.50 - 0.75}}{{1 - ( - 0.5 \times 0.75)}}c">
<msup>
<mi>u</mi>
<mo>′</mo>
</msup>
<mo>=</mo>
<mfrac>
<mrow>
<mo>−</mo>
<mn>0.50</mn>
<mo>−</mo>
<mn>0.75</mn>
</mrow>
<mrow>
<mn>1</mn>
<mo>−</mo>
<mo stretchy="false">(</mo>
<mo>−</mo>
<mn>0.5</mn>
<mo>×</mo>
<mn>0.75</mn>
<mo stretchy="false">)</mo>
</mrow>
</mfrac>
<mi>c</mi>
</math></span></p>
<p>–0.91<em>c</em></p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>nothing can travel faster than the speed of light (therefore (a)(ii) is the valid answer)</p>
<p> </p>
<p><em>OWTTE</em></p>
<p><strong><em>[1 mark]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>When a spaceship passes the Earth, an observer on the Earth and an observer on the spaceship both start clocks. The initial time on both clocks is 12 midnight. The spaceship is travelling at a constant velocity with <em>γ</em> = 1.25. A space station is stationary relative to the Earth and carries clocks that also read Earth time.</p>
</div>
<div class="specification">
<p>Some of the radio signal is reflected at the surface of the Earth and this reflected signal is later detected at the spaceship. The detection of this signal is event B. The spacetime diagram is shown for the Earth, showing the space station and the spaceship. Both axes are drawn to the same scale.</p>
<p style="text-align: left;"><img src="data:image/png;base64,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"></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate the velocity of the spaceship relative to the Earth.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>The spaceship passes the space station 90 minutes later as measured by the spaceship clock. Determine, for the reference frame of the Earth, the distance between the Earth and the space station.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>As the spaceship passes the space station, the space station sends a radio signal back to the Earth. The reception of this signal at the Earth is event A. Determine the time on the Earth clock when event A occurs.</p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Construct event A and event B on the spacetime diagram.</p>
<div class="marks">[3]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate, using the spacetime diagram, the time at which event B occurs for the spaceship.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>0.60<em>c</em></p>
<p><strong><em>OR</em></strong></p>
<p>1.8 × 10<sup>8</sup> <strong>«</strong>m s<sup>–1</sup><strong>»</strong></p>
<p> </p>
<p><em><strong>[1 mark]</strong></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p>time interval in the Earth frame = 90 × <em>γ</em> = 112.5 minutes</p>
<p><strong>«</strong>in Earth frame it takes 112.5 minutes for ship to reach station<strong>»</strong></p>
<p>so distance = 112.5 × 60 × 0.60<em>c</em></p>
<p>1.2 × 10m<sup>12</sup> <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p>Distance travelled according in the spaceship frame = 90 × 60 × 0.6<em>c</em></p>
<p>= 9.72 × 10<sup>11</sup> <strong>«</strong>m<strong>»</strong></p>
<p>Distance in the Earth frame <strong>«</strong>= 9.72 × 10<sup>11</sup> × 1.25<strong>»</strong> = 1.2 × 10<sup>12</sup> <strong>«</strong>m<strong>»</strong></p>
<p> </p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>signal will take <strong>«</strong>112.5 × 0.60 =<strong>»</strong> 67.5 <strong>«</strong>minutes<strong>»</strong> to reach Earth <strong>«</strong>as it travels at <em>c</em><strong>»</strong></p>
<p><strong>OR</strong></p>
<p>signal will take <strong>«</strong><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.2 \times {{10}^{12}}}}{{3 \times {{10}^8}}}">
<mfrac>
<mrow>
<mn>1.2</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mn>12</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>3</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span> =<strong>»</strong> 4000 <strong>«</strong><em>s</em><strong>»</strong></p>
<p> </p>
<p>total time <strong>«</strong>= 67.5 + 112.5<strong>»</strong> = 180 minutes <strong><em>or </em></strong>3.00 h or 3:00am</p>
<p> </p>
<p><strong><em>[2 marks]</em></strong></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line from event E to A, upward and to left with A on <em>ct </em>axis (approx correct)</p>
<p>line from event A to B, upward and to right with B on <em>ct' </em>axis (approx correct)</p>
<p>both lines drawn with ruler at 45 (judge by eye)</p>
<p> </p>
<p><em>eg:</em></p>
<p><img src="images/Schermafbeelding_2018-08-13_om_06.36.34.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/04.d.i/M"></p>
<p><strong><em>[3 marks]</em></strong></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong><em>ALTERNATIVE 1</em></strong></p>
<p><strong>«</strong>In spaceship frame<strong>»</strong></p>
<p>Finds the ratio <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{OB}}{{OE}}">
<mfrac>
<mrow>
<mi>O</mi>
<mi>B</mi>
</mrow>
<mrow>
<mi>O</mi>
<mi>E</mi>
</mrow>
</mfrac>
</math></span> (or by similar triangles on <em>x </em>or <em>ct </em>axes), value is approximately 4</p>
<p>hence time elapsed ≈ 4 × 90 mins ≈ 6h <strong>«</strong>so clock time is ≈ 6:00<strong>»</strong></p>
<p> </p>
<p><strong><em>Alternative 1:</em></strong></p>
<p><img src="images/Schermafbeelding_2018-08-13_om_06.33.50.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/04.d.ii/M"></p>
<p><em>Allow similar triangles using </em><em>x</em><em>-axis or ct-axis, such as </em><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{distance\,2}}{{distance\,1}}">
<mfrac>
<mrow>
<mi>d</mi>
<mi>i</mi>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>n</mi>
<mi>c</mi>
<mi>e</mi>
<mspace width="thinmathspace"></mspace>
<mn>2</mn>
</mrow>
<mrow>
<mi>d</mi>
<mi>i</mi>
<mi>s</mi>
<mi>t</mi>
<mi>a</mi>
<mi>n</mi>
<mi>c</mi>
<mi>e</mi>
<mspace width="thinmathspace"></mspace>
<mn>1</mn>
</mrow>
</mfrac>
</math></span><em> from diagrams below</em></p>
<p><em><img src="images/Schermafbeelding_2018-08-13_om_06.52.27.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/04.d.ii_02/M"></em></p>
<p> </p>
<p><strong><em>ALTERNATIVE 2</em></strong></p>
<p><strong>«</strong>In Earth frame<strong>»</strong></p>
<p>Finds the ratio</p>
<p><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{ct{\text{ coordinate of B}}}}{{ct{\text{ coordinate of A}}}}">
<mfrac>
<mrow>
<mi>c</mi>
<mi>t</mi>
<mrow>
<mtext> coordinate of B</mtext>
</mrow>
</mrow>
<mrow>
<mi>c</mi>
<mi>t</mi>
<mrow>
<mtext> coordinate of A</mtext>
</mrow>
</mrow>
</mfrac>
</math></span>, value is approximately 2.5</p>
<p>hence time elapsed ≈ <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{2.5 \times 3{\text{h}}}}{{1.25}}">
<mfrac>
<mrow>
<mn>2.5</mn>
<mo>×</mo>
<mn>3</mn>
<mrow>
<mtext>h</mtext>
</mrow>
</mrow>
<mrow>
<mn>1.25</mn>
</mrow>
</mfrac>
</math></span> ≈ 6h</p>
<p><strong>«</strong>so clocktime is ≈ 6:00<strong>»</strong></p>
<p> </p>
<p> </p>
<p><strong><em>ALTERNATIVE 2:</em></strong></p>
<p> <img src="images/Schermafbeelding_2018-08-13_om_06.53.38.png" alt="M18/4/PHYSI/SP3/ENG/TZ2/04.d.ii_03/M"></p>
<p> </p>
<p><em><strong>[2 marks]</strong></em></p>
<div class="question_part_label">d.ii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">d.ii.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">The speed of a spaceship is measured to be 0.50<em>c</em> by an observer at rest in the Earth’s reference frame.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Define an <em>inertial reference frame.</em></span></p>
<div class="marks">[1]</div>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">As the spaceship passes the Earth it emits a flash of light that travels in the same direction as the spaceship with speed <em>c</em> as measured by an observer on the spaceship. Calculate, according to the Galilean transformation, the speed of the light in the Earth’s reference frame.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Use your answer to (a)(ii) to describe the paradigm shift that Einstein’s theory of special relativity produced.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">a coordinate system which is not accelerating/has constant velocity/Newtons 1st law applies ✔</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;">OWTTE</span></em></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;">Both “inertial” and “reference frame” need to be defined</span></em></p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">1.5</span><em><span style="background-color:#ffffff;">c </span></em><span style="background-color:#ffffff;">✔</span></p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;"><em>c</em> is the same in all frames<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em>c</em> is maximum velocity possible ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">velocity addition frame dependent ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">length/time/mass/fields relative measurements ✔<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">Newtonian/Galilean mechanics valid only at low speed ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>In defining an inertial frame of reference far too many candidates started with the words ‘ a frame of reference that...... ’ instead of ‘a coordinate system that.....’</p>
<div class="question_part_label">ai.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Almost no incorrect answers were seen.</p>
<div class="question_part_label">aii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most candidates correctly stated that in special relativity the velocity of light, c, is the maximum possible velocity or is invariant. Only a few added that Galilean relativity only applies at speeds much less than the speed of light.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A spaceship moves away from the Earth in the direction of a nearby planet. An observer on the Earth determines the planet is 4 ly from the Earth. The spacetime diagram for the Earth’s reference frame shows the worldline of the spaceship. Assume the clock on the Earth, the clock on the planet, and the clock on the spaceship were all synchronized when<em> ct</em> = 0.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Show, using the spacetime diagram, that the speed of the spaceship relative to the Earth is 0.80<em>c</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Label, with the letter E, the event of the spaceship going past the planet.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the spaceship.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Determine, according to an observer on the spaceship as the spaceship passes the planet, the time shown by the clock on the planet.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">On passing the planet a probe containing the spaceship’s clock and an astronaut is sent back to Earth at a speed of 0.80<em>c</em> relative to Earth. Suggest, for this situation, how the twin paradox arises and how it is resolved.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;"><em>Evidence of finding 1/gradient such as:</em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">use of any correct coordinate pair to find <em>v</em> - eg <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{4}{5}">
<mfrac>
<mn>4</mn>
<mn>5</mn>
</mfrac>
</math></span> or <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{6}{{7.5}}">
<mfrac>
<mn>6</mn>
<mrow>
<mn>7.5</mn>
</mrow>
</mfrac>
</math></span>.<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">measures tan of angle between <em>ct</em> and <em>ct</em>’ as about 39° <em><strong>AND</strong> </em>tan 39 <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">≈</span> 0.8 ✔</span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><em>Answer 0.8c given, so check coordinate values carefully.</em><br></span></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">E labelled at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span><em> </em>= 4, <em>ct</em> = 5 ✔</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Check that E is placed on the worldline of S.</span></span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><img src="data:image/png;base64,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" width="111" height="95"></span></span></p>
<p style="text-align:left;"><em><strong><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">OR</span></span></strong></em></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><img src="data:image/png;base64,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" width="88" height="18"></span></span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Allow solutions involving the use of Lorentz equations.</span></span></span></em></p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><em>t <span style="background-color:#ffffff;">= </span></em><span style="background-color:#ffffff;">5 </span><span style="background-color:#ffffff;">years</span><em><span style="background-color:#ffffff;"><strong> OR</strong> ct = </span></em><span style="background-color:#ffffff;">5 </span><span style="background-color:#ffffff;">ly</span><em><span style="background-color:#ffffff;"> ✔</span></em></p>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">On return to Earth the astronaut will have aged less than Earthlings «by 4 years»<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">time passed on Earth is greater than time passed for the astronaut «by 4 years» <span style="display:inline !important;float:none;background-color:#ffffff;color:#000000;font-family:Verdana , Arial , Helvetica , sans-serif;font-size:14px;font-style:normal;font-variant:normal;font-weight:400;letter-spacing:normal;text-align:left;text-decoration:none;text-indent:0px;white-space:normal;">✔</span><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">astronaut accelerated/changed frames but Earth did not<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">for astronaut the Earth clock jumps forward at turn-around ✔</span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">OWTTE<br></span></span></em></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">Treat as neutral any mention of both the Earth and astronaut seeing each other’s clock as running slow.</span></span></em></p>
<div class="question_part_label">d.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Most candidates could show that the velocity of the spacecraft was 0.8c.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Event E was usually correctly labelled on the space-time diagram.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A very simple time dilation question which most candidates got wrong at SL but the question was better answered at HL.</p>
<div class="question_part_label">ci.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates tried to use time dilation again without realising that the clock on P must also read 5 years at event E because that is the time on the Earth clock in P’s frame for the event.</p>
<div class="question_part_label">cii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The twin paradox is now well understood and there were some good quality answers. Some candidates even knew that the Earth clock jumps forward when the Astronaut turns around.</p>
<div class="question_part_label">d.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A train of proper length 85 m moves with speed 0.60<em>c</em> relative to a stationary observer on a platform.</span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Define <em>proper length</em>.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">In the reference frame of the train a ball travels with speed 0.50<em>c</em> from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the train.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">In the reference frame of the train a ball travels with speed 0.50<em>c</em> from the back to the front of the train, as the train passes the platform. Calculate the time taken for the ball to reach the front of the train in the reference frame of the platform.</span></p>
<div class="marks">[3]</div>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">the length measured «in a reference frame» where the object is at rest ✔<br></span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><img src="data:image/png;base64,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" width="304" height="47"><span style="background-color:#ffffff;"><br></span></p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><em><strong><span style="background-color:#ffffff;">ALTERNATIVE 1:</span></strong></em><span style="background-color:#ffffff;"><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><img src="data:image/png;base64,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" width="265" height="115"></span></p>
<p style="text-align:left;"><em><strong><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">ALTERNATIVE 2:</span></span></strong></em></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><em>v</em> of ball is 0.846<em>c</em> for platform ✔<br></span></span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">length of train is 68m for platform ✔</span></span></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><img src="data:image/png;base64,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" width="468" height="45"></span></span></span></p>
<p style="text-align:left;"><em><strong><span style="background-color:#ffffff;"><span style="background-color:#ffffff;"><span style="background-color:#ffffff;">ALTERNATIVE 3:</span></span></span></strong></em></p>
<p style="text-align:left;"><img src="data:image/png;base64,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" width="511" height="121"></p>
<div class="question_part_label">bii.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Proper length is quite well understood. A common mistake is to mention that it is the length measured by a reference frame at rest.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Because there were three frames of reference in this question many candidates struggled to find the simple value for the time of the ball’s travel down the train in the train’s frame of reference.</p>
<div class="question_part_label">bi.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Almost no candidates could use a Lorentz transformation to find the time of the ball’s travel in the frame of reference of the platform. Most just applied some form of t=γt’. Elapsed time and instantaneous time in different frames were easily confused. Candidates rarely mention which reference frame is used when making calculations, however this is crucial in relativity.</p>
<div class="question_part_label">bii.</div>
</div>
<br><hr><br><div class="specification">
<p>A rocket moving with speed v relative to the ground emits a flash of light in the backward direction.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">An observer in the rocket measures the speed of the flash of light to be <em>c</em>.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Galilean relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Maxwell’s theory of electromagnetism.</p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>State the <strong>speed</strong> of the flash of light according to an observer on the ground using Einstein’s theory of relativity.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><em>c–v</em> ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>c</em> ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em>c</em> ✔</p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>The speed of a flash of light from different viewpoints. Most of the prepared candidates well stated the speed of the flash using Galilean relativity, Maxwell’s theory and Einstein’s theory.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The speed of a flash of light from different viewpoints. Most of the prepared candidates well stated the speed of the flash using Galilean relativity, Maxwell’s theory and Einstein’s theory.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>The speed of a flash of light from different viewpoints. Most of the prepared candidates well stated the speed of the flash using Galilean relativity, Maxwell’s theory and Einstein’s theory.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="specification">
<p>The diagram shows space and time axes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> and <em>ct</em> for an observer at rest with respect to a galaxy. A spacecraft moving through the galaxy has space and time axes <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>′ and <em>ct</em>′.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p style="text-align: left;">A rocket is launched towards the right from the spacecraft when it is at the origin of the axes. This is labelled event 1 on the spacetime diagram. Event 2 is an asteroid exploding at <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span> = 100 ly and <em>ct</em> = 20 ly.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot, on the axes, the point corresponding to event 2.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Suggest whether the rocket launched by the spacecraft might be the cause of the explosion of the asteroid.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Show that the value of the invariant spacetime interval between events 1 and 2 is 9600 ly<sup>2</sup>.</p>
<div class="marks">[1]</div>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>An observer in the spacecraft measures that events 1 and 2 are a distance of 120 ly apart. Determine, according to the spacecraft observer, the time between events 1 and 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Using the spacetime diagram, determine which event occurred first for the spacecraft observer, event 1 or event 2.</p>
<div class="marks">[2]</div>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine, using the diagram, the speed of the spacecraft relative to the galaxy.</p>
<div class="marks">[2]</div>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p>point as shown ✔</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><strong>ALTERNATIVE 1</strong><br>the rocket would have to travel faster than the speed of light ✔</p>
<p>so impossible ✔</p>
<p><strong>ALTERNATIVE 2</strong><br>drawing of future lightcone at origin ✔</p>
<p>and seeing that the asteroid explodes outside the lightcone so impossible ✔</p>
<p><strong>ALTERNATIVE 3</strong><br>the event was observed at +20 years, but its distance (stationary) is 100 ly ✔</p>
<p>so the asteroid event happened 80 years before t = 0 for the galactic observer ✔</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>100<sup>2</sup> − 20<sup>2</sup> = 9600 «ly<sup>2</sup>» ✔</p>
<p><em>Also accept 98 (the square root of 9600).</em></p>
<p><em>Allow negative value.</em></p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>9600 = 120<sup>2</sup> − <em>c</em><sup>2</sup><em>t</em><sup>2</sup> ✔</p>
<p><em>ct</em> = «−» 69.3 «ly» /<em> t = «−» 69.3 «y» </em>✔</p>
<p><em>Allow approach with Lorentz transformation.</em></p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>line from event 2 parallel to <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="x">
<mi>x</mi>
</math></span>’ axis intersects <em>ct</em>’ axis at a negative value ✔</p>
<p>event 2 occurred first ✔</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>use of tan <em>θ </em>= <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{v}{c}">
<mfrac>
<mi>v</mi>
<mi>c</mi>
</mfrac>
</math></span> with the angle between the time axes ✔</p>
<p>to get (0.70 ± 0.02)<em>c</em> ✔</p>
<div class="question_part_label">e.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Almost all candidates were able to plot the event on the diagram.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most of the candidates identified, that the spacecraft was launched after the asteroid explosion and better candidates were also able to explain their reasoning with a drawing of light cones on the spacetime graph being the most popular response type.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference. </p>
<div class="question_part_label">c.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference. </p>
<div class="question_part_label">d.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most of the candidates well used the formula for invariant spacetime from the data booklet, but only a few strong candidates were able to determine the time between the events according to the spacecraft observer. This implies a lack of understanding of the concept of invariance for different frames of reference. Most candidates well determined that event 2 occurred first in d ii), with a lesser number showing this correctly via the spacetime diagram.</p>
<div class="question_part_label">d.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Many candidates determined the speed using the spacetime diagram. However, some experienced difficulties reading accurately from the graph, and though their approach was correct, they failed to gain a result within the accepted range of values.</p>
<div class="question_part_label">e.</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A long straight current-carrying wire is at rest in a laboratory. A negatively-charged particle P outside the wire moves parallel to the current with constant velocity<em> v</em> relative to the laboratory.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">In the reference frame of the laboratory the particle P experiences a repulsive force away from the wire.</span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">One of the two postulates of special relativity states that the speed of light in a vacuum is the same for all observers in inertial reference frames. State the other postulate of special relativity.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">State the nature of the force on the particle P in the reference frame of the laboratory.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Deduce, using your answer to part (a), the nature of the force that acts on the particle P in the rest frame of P.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Explain how the force in part (b)(ii) arises.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">The velocity of P is 0.30<em>c</em> relative to the laboratory. A second particle Q moves at a velocity of 0.80<em>c</em> relative to the laboratory.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Calculate the speed of Q relative to P.</span></span></p>
<div class="marks">[2]</div>
<div class="question_part_label">b(iv).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">laws of physics are the same for all observers<br><em><strong>OR</strong></em><br>laws of physics are the same in all «inertial» frames ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: OWTTE</span></em></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">magnetic ✔</span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">«from 3a»<br>force must still be repulsive ✔</span></p>
<p><span style="background-color: #ffffff;">for P there is no magnetic force <em><strong>AND</strong> </em>force is electric/electrostatic<br><em><strong>OR</strong></em><br>since P is at rest the force is electric/electrostatic ✔</span></p>
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;">protons and electrons in the wire move with different velocities «relative to P»<br><em><strong>OR</strong></em><br>speed of electrons is greater ✔</span></p>
<p><span style="background-color: #ffffff;">«for P» the density of protons and electrons in wire will be different «due to length contraction»<br><em><strong>OR</strong></em><br>«for P» the wire appears to have negative charge «due to length contraction» ✔</span></p>
<p><span style="background-color: #ffffff;">«hence electric force arises»<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Do not award mark for mention of length contraction without details.</span></em></p>
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>u</mi><mo>'</mo><mo>=</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>80</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>30</mn></mrow><mrow><mn>1</mn><mo>+</mo><mn>0</mn><mo>.</mo><mn>80</mn><mo>×</mo><mn>0</mn><mo>.</mo><mn>30</mn></mrow></mfrac><mi>c</mi></math> </span></em><span style="background-color: #ffffff;">✔</span></p>
<p><em><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>=</mo><mn>0</mn><mo>.</mo><mn>89</mn><mi>c</mi></math> </span></em><span style="background-color: #ffffff;">✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Accept 0.89c if all negative values used. Accept –0.89c even though speed is required.</span></em></p>
<div class="question_part_label">b(iv).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b(iv).</div>
</div>
<br><hr><br><div class="specification">
<p>Muons are created at a height of 3230 m above the Earth’s surface. The muons move vertically downward at a speed of 0.980 c relative to the Earth’s surface. The gamma factor for this speed is 5.00. The half-life of a muon in its rest frame is 2.20 μs.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to Newtonian mechanics.</p>
<div class="marks">[3]</div>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Estimate in the Earth frame the fraction of the original muons that will reach the Earth’s surface before decaying according to special relativity.</p>
<div class="marks">[2]</div>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Demonstrate how an observer moving with the same velocity as the muons accounts for the answer to (a)(ii).</p>
<div class="marks">[2]</div>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p>time of travel is «<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{3230}}{{0.98 \times 3.0 \times {{10}^8}}}">
<mfrac>
<mrow>
<mn>3230</mn>
</mrow>
<mrow>
<mn>0.98</mn>
<mo>×</mo>
<mn>3.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span>» = 1.10 × 10<sup>−5</sup> «s» ✔</p>
<p>which is «<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.10 \times {{10}^{ - 5}}}}{{2.20 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>1.10</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>2.20</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span>» = 5.0 half-lives ✔</p>
<p>so fraction arriving as muons is « <span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{{{2^5}}}">
<mfrac>
<mn>1</mn>
<mrow>
<mrow>
<msup>
<mn>2</mn>
<mn>5</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span> » = <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{32}">
<mfrac>
<mn>1</mn>
<mn>32</mn>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>3 % ✔</p>
<p><em>Award<strong> [3]</strong> for a bald correct answer</em>.</p>
<p> </p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>time of travel corresponds to «<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{1.10 \times {{10}^{ - 5}}}}{{5.0 \times 2.20 \times {{10}^{ - 6}}}}">
<mfrac>
<mrow>
<mn>1.10</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>5</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mrow>
<mn>5.0</mn>
<mo>×</mo>
<mn>2.20</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
</mfrac>
</math></span></span>» = 1.0 half-life ✔</p>
<p>so fraction arriving as muons is <span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{1}{2}">
<mfrac>
<mn>1</mn>
<mn>2</mn>
</mfrac>
</math></span></p>
<p><em><strong>OR</strong></em></p>
<p>50 % ✔</p>
<p><em>Award<strong> [2]</strong> for a bald correct answer</em>.</p>
<p> </p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>observer measures the distance to the surface to be shorter «by a factor of 5.0»/ length contraction occurs ✔</p>
<p>so time of travel again corresponds to «<span style="background-color:#ffffff;"><span class="mjpage"><math xmlns="http://www.w3.org/1998/Math/MathML" alttext="\frac{{\left( {\frac{{\frac{{3230}}{{5.0}}}}{{0.98 \times 3.0 \times {{10}^8}}}} \right)}}{{\left( {2.20 \times {{10}^{ - 6}}} \right)}}">
<mfrac>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mfrac>
<mrow>
<mfrac>
<mrow>
<mn>3230</mn>
</mrow>
<mrow>
<mn>5.0</mn>
</mrow>
</mfrac>
</mrow>
<mrow>
<mn>0.98</mn>
<mo>×</mo>
<mn>3.0</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mn>8</mn>
</msup>
</mrow>
</mrow>
</mfrac>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
<mrow>
<mrow>
<mo>(</mo>
<mrow>
<mn>2.20</mn>
<mo>×</mo>
<mrow>
<msup>
<mrow>
<mn>10</mn>
</mrow>
<mrow>
<mo>−</mo>
<mn>6</mn>
</mrow>
</msup>
</mrow>
</mrow>
<mo>)</mo>
</mrow>
</mrow>
</mfrac>
</math></span></span>»= 1.0 half-life ✔</p>
<div class="question_part_label">b.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Muons. The problem of muons created above the Earth surface moving almost at the speed of light, explicitly mentioned in the Guide, was solved well by prepared candidates. In i) many correctly calculated the time of travel in the earth’s frame though some struggled to recognize and apply the decay half-life aspect of this problem.</p>
<div class="question_part_label">a.i.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Students who correctly answered part i) did so in ii).</p>
<div class="question_part_label">a.ii.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Some candidates struggled in b), with only the best candidates identified length contraction. Importantly, the command term here is “demonstrate” which means students must make their response clear by reasoning or evidence. Many who identified length contraction did not provide adequate reasoning to gain full marks.</p>
<div class="question_part_label">b.</div>
</div>
<br><hr><br><div class="specification">
<p>The spacetime diagram is in the reference frame of an observer O on Earth. Observer O and spaceship A are at the origin of the spacetime diagram when time <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mi>t</mi><mo>'</mo><mo>=</mo><mn>0</mn></math>. The worldline for spaceship A is shown.</p>
<p style="text-align: center;"><img src="data:image/png;base64,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"></p>
<p> </p>
</div>
<div class="specification">
<p>Event E is the emission of a flash of light. Observer O sees light from the flash when <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn>9</mn></math> years and calculates that event E is <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn><mo> </mo><mi>ly</mi></math> away, in the positive <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math> direction.</p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Calculate in terms of <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi></math> the velocity of spaceship A relative to observer O.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Draw the <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi><mo>'</mo></math> axis for the reference frame of spaceship A.</p>
<div class="marks">[1]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Plot the event E on the spacetime diagram and label it E.</p>
<div class="marks">[2]</div>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p>Determine the time, according to spaceship A, when light from event E was observed on spaceship A.</p>
<div class="marks">[3]</div>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0"><math xmlns="http://www.w3.org/1998/Math/MathML"><mn>0</mn><mo>.</mo><mn>6</mn><mi mathvariant="normal">c</mi></math> </span><span class="fontstyle2">✓ </span></p>
<p><em><span class="fontstyle3">Accept <math xmlns="http://www.w3.org/1998/Math/MathML"><mn mathvariant="italic">1</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">8</mn><mo mathvariant="italic">×</mo><mn mathvariant="italic">10</mn><msup><mo mathvariant="italic"> </mo><mn mathvariant="italic">8</mn></msup><mo> </mo><mi>m</mi><msup><mi>s</mi><mrow><mo mathvariant="italic">-</mo><mn mathvariant="italic">1</mn></mrow></msup></math></span><span class="fontstyle3"> </span><span class="fontstyle3">if unit given.</span></em></p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">line through origin and through <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>(</mo><mn>5</mn><mo>,</mo><mo> </mo><mn>3</mn><mo>)</mo><mo> </mo><mo>±</mo></math> one small square at this coordinate </span><span class="fontstyle2">✓</span></p>
<p><img src="data:image/png;base64,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"></p>
<p><em><span class="fontstyle0">Answers shown for 5(a)(ii) and (b)(i) and (b)(ii).</span></em></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">X value of E at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>4</mn></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi>ly</mi></math>» </span><span class="fontstyle2">✓<br></span></p>
<p><span class="fontstyle0">Y value of E at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>5</mn></math> «<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi></math>» </span><span class="fontstyle2">✓</span></p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span class="fontstyle0">light cone from E «crosses </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>t</mi></math> </span><span class="fontstyle0">at <math xmlns="http://www.w3.org/1998/Math/MathML"><mn>9</mn></math> so» intersection on </span><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>t</mi><mo>'</mo><mo>=</mo><mn>5</mn><mo>.</mo><mn>6</mn><mo>±</mo><mn>0</mn><mo>.</mo><mn>2</mn></math> <math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi></math><span class="fontstyle0"> «on </span><span class="fontstyle2"><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>c</mi><mi>t</mi></math> </span><span class="fontstyle0">scale» </span><span class="fontstyle3">✓</span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>25</mn></math> <span class="fontstyle3">✓</span></p>
<p><span class="fontstyle0">so <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>'</mo><mo>=</mo><mo>«</mo><mfrac><mrow><mn>5</mn><mo>.</mo><mn>6</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>25</mn></mrow></mfrac><mo>=</mo><mo>»</mo><mo> </mo><mn>4</mn><mo>.</mo><mn>5</mn></math> </span><span class="fontstyle0">«<math xmlns="http://www.w3.org/1998/Math/MathML"><mi mathvariant="normal">y</mi></math> after leaving Earth» </span><span class="fontstyle3">✓</span></p>
<p> </p>
<p><em><span class="fontstyle2">MP1 accept use of linear equations to find <math xmlns="http://www.w3.org/1998/Math/MathML"><mi>t</mi><mo>=</mo><mn mathvariant="italic">5</mn><mo mathvariant="italic">.</mo><mn mathvariant="italic">625</mn></math></span></em></p>
<p><em><span class="fontstyle2">Allow ECF from (b)(i) and (a)</span></em></p>
<div class="question_part_label">b(ii).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Very well answered.</p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Most answers successfully drew the correct x' axis.</p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Event E is the event when the light is emitted (4,5). Some candidates missed that and placed it at (4,9).</p>
<p>To determine these coordinates candidates were expected to construct a light path from (0,9) which intercepts at x=4 and t=5. This is a very common mistake which needs careful explanation by teachers.</p>
<div class="question_part_label">b(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Those candidates who placed E at the correct position were then able to calculate the time appropriately.</p>
<div class="question_part_label">b(ii).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">A train is moving across a bridge with a speed <em>v</em> = 0.40<em>c</em>. Observer A is at rest in the train. Observer B is at rest with respect to the bridge.</span></p>
<p><span style="background-color: #ffffff;">The length of the bridge<em> L</em><sub>B</sub> according to observer B is 2.0 km.</span></p>
</div>
<div class="specification">
<p><span style="background-color: #ffffff;">According to observer B, two lamps at opposite ends of the bridge are turned on simultaneously as observer A crosses the bridge. Event X is the lamp at one end of the bridge turning on. Event Y is the lamp at the other end of the bridge turning on.</span></p>
<p style="text-align: center;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">Events X and Y are shown on the spacetime diagram. The space and time axes of the reference frame for observer B are <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math></em> and <em>ct</em>. The line labelled <em>ct'</em> is the worldline of observer A.</span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, for observer A, the length<em> L</em><sub>A</sub> of the bridge</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Calculate, for observer A, the time taken to cross the bridge.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Outline why<em> L</em><sub>B</sub> is the proper length of the bridge.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Draw, on the spacetime diagram, the space axis for the reference frame of observer A. Label this axis <em><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>x</mi></math>'</em>.</span></p>
<p> </p>
<div class="marks">[1]</div>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Demonstrate using the diagram which lamp, according to observer A, was <strong>turned on</strong> first.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Demonstrate, using the diagram, which lamp observer A <strong>observes</strong> to light first.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iii).</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color: #ffffff;">Determine the time, according to observer A, between X and Y.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c(iv).</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mi>γ</mi><mo>=</mo><mn>1</mn><mo>.</mo><mn>09</mn></math><span style="background-color: #ffffff;">✔</span></p>
<p><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>L</mi><mi mathvariant="normal">A</mi></msub><mo>=</mo><mo>«</mo><mfrac><mrow><mn>2</mn><mo>.</mo><mn>0</mn></mrow><mrow><mn>1</mn><mo>.</mo><mn>09</mn></mrow></mfrac><mo>=</mo><mo>»</mo></math> 1.8 «km» ✔</span></p>
<p> </p>
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong><span style="background-color: #ffffff;">ALTERNATIVE 1</span></strong></em></p>
<p><span style="background-color: #ffffff;">time = <math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mrow><mn>1</mn><mo>.</mo><mn>8</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></math>✔</span></p>
<p><span style="background-color: #ffffff;">1.5 × 10<sup>–5 </sup></span>«s» ✔</p>
<p> </p>
<p><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">ALTERNATIVE 2</span></p>
<p><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mi mathvariant="normal">B</mi></msub><mo>=</mo><mfrac><mrow><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>1</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>66</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">«s» ✔</span></span></p>
<p><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"><math xmlns="http://www.w3.org/1998/Math/MathML"><msub><mi>t</mi><mi mathvariant="normal">A</mi></msub><mo>=</mo><mfrac><msub><mi>t</mi><mi mathvariant="normal">B</mi></msub><mi>γ</mi></mfrac><mo>=</mo><mn>1</mn><mo>.</mo><mn>5</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>5</mn></mrow></msup></math> «s» ✔</span></span></p>
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><span style="background-color: #ffffff;"><em style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: italic;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">L</em><sub style="color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 11.6px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">B</sub> is the length/measurement «by observer B» made in the reference frame in which the bridge is at rest ✔<br></span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Idea of rest frame or frame in which bridge is not moving is required.</span></em></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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" width="302" height="260"></p>
<p><span style="background-color: #ffffff;"><em>x′</em> axis drawn with correct gradient of 0.4 ✔</span></p>
<p> </p>
<p><em><span style="background-color: #ffffff;">NOTE: Line must be 1 square below Y, allow ±0.5 square.<br></span></em></p>
<p><em><span style="background-color: #ffffff;">Allow line drawn without a ruler.</span></em></p>
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAYMAAAFSCAYAAAAQBrOYAAAAAXNSR0IArs4c6QAAAARnQU1BAACxjwv8YQUAAAAJcEhZcwAADsMAAA7DAcdvqGQAANgMSURBVHhe7L0NnFVV1T++uJy53BlmYEYYBRVpIiIiVMxXUlIyMjI0LC0trcd6zNSkJMTU0nwJDYtKK0ufsiLzBVJSUlIiVDQ0MEknnHDEEQcYcAbn7c6dw53/+u5zznDmzr13zr37+xC/5+93PnDPPfvcffZee+2911577bUG9SjkbbyNt/E23sb/rxHzP9/G23gbb+Nt/P8Yb08Gb+NtvI238Tbengzextt4G2/jbbw9GbyNt/E23sbbUPTbQG5v7ZS0/hmUpES645LqSEl8uH7XawN3iIjT5V0D/nMG4bTwfYWb1O8xV5x4mbmOJxLippMyZIgj3d06L6VdTXdyp6WHSjrWKr/+7e/klJkz5MCRo7Sk/nyW6705yhrTX77VlpSyhF47Tr+yRsrPv2/oU6bpAzzXixxpYfp4NyKUAQillbiDpV3/HP2LlWo74n6Idk4sN12Rli5JinQpdWIxeePV16Vm/MHec0ARdcL9VHqnxOPlecsdJe9kW5tUVJVlLw8QIb+87R6hDAZ+Wr9+AeTKI09ZW1reFDflyv77Kz+D/hF+k+09oE9Z+bDceYR/D+RIM3yopIkrfUz/ypXHAHlnbfeIZQjf79PuOfg1c9zIlpZMdZj8yssO2PNOoIA6IS2VapOhseHS7ez27hdRJ9x3d6XFKUv0fi+kDAZ+WpgPwd+DS7zkRKLCu4iI3NZE/sAMJJOtfTN2lciOX4nQcwbhNCAjn5gTVybTChUDzfu/v/o12bVzh74iLqfPPF0+ddan/ERFZlnC3zPTFG4yqQ3qSCkGhQD5fpMjrR99isgD6EOffHnko78imeoUxynVDuHfKBL1mzZJzbhx3pd85cmXpjD0iZd6aUXwTZDWntwlQxPgekW+d+ZLU6Ddd8cdGRL1NznSCmr3PG3W2NCgaY6MHj3au5EvnzxpaHdD5wDF5pNsk0HxRF/6AJl55GszRdZ2B8LP5cvDv27VwbcCk4oltm1r0vZyZPjwqn5lzfbeXmR8b012SEXCF9gKySejrsxxo9CBPxtyDxehl/nrhD0IN164wEA4DchMj/nTVoFY+9xaOfToqXLu2efImIPGyuK7FktLR4vcc889/hOKfu8Kfc9MU7S5ndJvWsr3mzxpfWhUZB6iA3hMBnnXeZ/LQ38fKgv5V8WDUidA76Vxv1i+8dMGxUISUjg9M698aYo2/Tc47Ut1AYrMrw+V8+WRp+6OkzHQ5csnT5qbzuipxebj9vSnD5CZR742A/R7v3YHws/lS/OvhwR9goBYwEPh9wBZ3tuLjO9DJCQ/F5JPlroy+pibZxgvBJFywUTEQYWkMxk2Ir74lTnywrp1cvzxx+vSyrv3pS98SZYtXyZ1dbXejUJhBl9O5RjNkVDp0HX9JaAFnFipkRJtkU5xmAwMxMgpxmNEnSw5x2syumxRcEtb/Cs7ZAwtRcNxKrRXDPa/WYDU7ql0kZqEDKTBP1CtWKJXjW4LLQ+DpVntHqmtwloUO7QVVfAmXd796uc/8b8pDVN7CvSjRT+S1vYiB1BdGaQJ3Rk1KnKO64O2pHJGpkRQBNLpLnHiQ/1vxSMWJzG91qmf1FoEGG0FJNxWHewypLQigBq5jPmplVMvFn20QJpTlpVBoSC1uyP2gg3gaHm0a1iDJYkDMUJWrHaPVJRUWuVnilBWrsxROJNVH1AtRxx+uP8N2DO7j6gakZEWHUYCKqI8mWCxBjZ9nRhBIgPS3f6FBRgzHGAkRAbXU5hQkqbz2I8KtHYn6HsNSPQxfb1IdW4fkNo9LYSyKIxETxC2HFK3YJSFiUgtFY/p3EMod0J0OUxgsnSK0xpusknicfslKDoPY4YHfRhqonQ6pe1lX68UVioMOKWUeYU1NyWcKv2f0+6MfuGWNPtXdmDRx3XbNDMCQ5PaPaYrOQagoo6VEHhax0MKMFkSyBxDexEQqShoUMbKoE1XBg5hnRaL2y/xAWzcUXT0OiAwmN6oLrQD2QKbZCnXvkBOgiS5uJ0cpifkASTdZmV8e4ZGu9v2C8M3nfaWMgBLneskqin0YbW7GyPRh6QmYq1UsDKgjBsk+kRqKjQoZ2XgasEJm0Gk5TDAaFg0KIXpMRloB7IFlsOMTSXS2LvPAXzI0LOi3W37heEbmBwS4KY5s4EjSYr6lAWWkQcNDBUsQBrH9roRTJLAr1jMoCPaIma5MGhsbDSfrlMiKkOb6zBgt3vVVVfJypUr/Tt7gPvLlz/of/MQi5eqtEliWMLKAEzGGOxirJWBgiEBpWME2igS5dUq0durHtDuLYSOUVpBojNDz6/Anko8xrG22pfa3YVaJm2/P8MqD8CgD/iQgUiTAQqcIGhmEvqXTNszmesdJCwYna2t8pGPfURuv/12891xu3UqCNmu+1i58im54YYbpKlpi39nD3B/1cqn/W8e0qlO7Tz2HRoSGUXq0LIwpIU0a88A5WEsM0gSWUtbM8XaCu1enmk7XgS6uzmdmWV1w7KyY7U7Q7UMGDVRjCAEpEl0JtHHTXH6BaOLFoA2faG9tUysyO182DasWL7C/6bM4QzKOsCsXbvGfJ5yyizzmQls0IZBGegUrikhwZqIJCEShBYP+9hyGIgRRDJau6tQwgBPTQQlI6H1Wepc1oYtC6T+9f+smoijBcFGh/3KIO3mLnZd3Uty1hlnSUlJiQwaNMj8O+dznzMbxaMOHmmegXS/4OaFhumz4de/XCxXXn69DB/uuz7IQFh9cs8998mEcYfK5vo68720tFR++uOf9r67ekSV3LN4mXzn+u/03jvkne+U5597zjzfF+XaBe11tZCkKGoi/3NvAafMA6xatcr8+99Awimh0IexxMeA4JRy9gxYgwLUpxRTYBJg2s4AT7jhTN5YGTDgkKSSSLngXZwN5JZ+UnVRyEPE2374c7l36b3yqzt+JnC7dMetd8jvfvtbWb36Kbn5xoXmmVkzZsmMj07X4SApsUzTUjcp9a+9Iuefd7Z/oz8CqXLNmjXy6U+fKzfevEBqxo0395LJpPzyNz+VN17plM7Ot6R67Bj59GdPk4eW3S9vbn9Tliz5lTTU18vv7/+9eT4MY3pLkBYYB32AvW1aesxRH/Svsk8GpGqZPSEGKP1Cedltrva/2CFOklgrtV8Qemnkdh8I8Zi9Sg/ACeTYUHuVHIvO6OuMcbyDoU1QRCoKqxPSTCdzqIkg/d/+yztl0cJFcs5555t75190vlxx9eVK9Lic+9nPmnuTj5osR0w+wmyUpTNMMJevXC0TJ02Umok1/p3+SLuO3H333fKhD31IvnzRf8kZn+qrTvrmFd+W0TUJ4zxq1skzzb1vXXmzVFVXyaxZnzbfk239B1oWfWgSx143Le0rITsZIy1JAELFeFI0I5sEZ3JKkSTWNncwZ2VAMi3FiWgGYlqYdLu9vj/JWmNoP6VMlqR2j9xUDKbHYMfYDMp16Gy3Zp3saJMLdIAO48bvLJATTzze/7YHZvDNIOTKRx6Rk2fM8L9lx8pVj8nZZ58tifJKueaKb5kZPoxTP36qf6X93HdRO/O0U8xncBgMlg2ZwOQUI5x7ABiDHWvsDZg+2ZyUi79yoQwfXmH+QZ2H/ZlHlObnnHeOeTT4rKoeLeMn+B5T/xewz6iJFOaQ174EFUiyWdn9p8Ay1GOpvhyCEYwBQQsAxBjm+opI1MHszlATAYxzBoGjukz0DPYYOKc716F9321OIGeY0K197jk57LAp/rfs+Pvf/y6XX3q5tOzYKj/9xU9N5wkj2+nfVIZqIttkYDbuCCeHscFFmQxYKwOtK/jnvR+YKrf99Gfyhz88KN//0a1Gnff5z35RNm7aLL/79e/Mo8HnpRddIGd96jPmOgDNpE/by1huWQL9gjFQVVTYWyQBNBNM7Reeyw57MCZMJ8Gpl7EmIsxxSZbLGAWDPoyDs0DkqZLB9CzTyVympY7jmYliEzmMdc8/L3ffc3e/JSJOIIdNSzs1/YknnpDZs/ZI9tlw+qxZsmDRArn1Z7fKD35wizRtafBTciPTlBGMmQmaaakuz82qxxJM09Llyx+R+tr18pOf/ECmT58u5593njz88AMSH1ZmBv4grEau8BoGpOUwHNVlMykuBgwhiWVayjJ5TCRGa14cR3UMNRFMeBlIukmKgMNSy7DoY4I0EdAvuE3m5hrM1bq6XBlcosOLvhQzGf6FK4HrYIYLp4XvAylIiKDjkIQOhm7W3wBZ88OsrjOSE3fkqnlXyDULFmp37tJBDw9rXioVxaRbTjvtNNlY92/5+c9/JtOOP0E2btggF17yVTn55JN10LlE9j9wlHzta5fJ9TdeJyllDuzEmz/NBucLLrzwAp1MXtb8BvcyYVAGEL10CAavS+XmRTfp7wfLt66aK3Ub6uTuB++FXC+lpcOks0tnK0j+WuYFN94k1157rbS2t2gecZMP8rjowovkJs1jsGYe1DVMH0j2eLYfHRTh+0A4DXRIu+3e93TMDFZBevAbXGNyz0wL8jDQsm+ue13GjhtlvuKnQTKezXw+nH84zUirna3y/R/+VL597ZWyfcebMnQo2n+wpFJdZgLHs1jqlpQMUl5LGtpDXWbaVgFamHcqHzqlfRk/eCcQfm+u8qBeXa0lUjJUaaR/kX6jyExDPt1daRlUkurtF0Fa1PywXYUARE3NbfolJdXV+/mpexD8Hhgo75SWJ1HqPRCkBc+Z94XaPF8aInk58Ur94vFg8BwQPA/kug+g3d32XRIv9do313O50oL7UOe5XUrjUL3Cvwmu8Zmtfr3Q1eDObdvMeSBETSsGyB9jQKpzT3kC4JW4k/kJBNf6c7PeQp0wlhnDwRLEkvPGn6h1ykxLtmt5hsZNvuYZx9vgBl8WBEwGA6Gz8y3/yg6dnT093d3+Fwtcdtnl/lV//P1vf8fk1udfeWJUz5vb3zT1CO7pgK4Fau7pDBXo8ssv6/n2t7/tf8sO/BbPBXjrzW5z7+VXXjbfcR0G8su81/v+DIA+4fIUC2TBoPPLr7zkX9kBdM9Gh0wMlN7ayuHD5uY3KPRh9AuU45WXXunZrvxpCwbvAM3KiBT6aCaMfLrRMQh44403KG1GKg6lLEBrJ6fddX4ZGOluzgYFJiqXsJSNxXIr/o44+gjRRpcf3Xqr6AAk3/3ud+WvT//RWPJgL+Gpvz0l1113nRxz3DGSlME6l+6ZPY865jg58cQT/W/ZgTynz/A2g4GKKkd+/atfyeZN9eY70sNAfrgX1uvh+8mnnOx/2wNj6kpYnmNlQEGSo8uGFJ0o85xpNW7pe6p75SMrpLU1orWI5sMAI0SggZYH0pkN0CfKKys1H/s9jLTb3StB2gAn8ynWVmnNJ9IIkx8pwtmkAL3xsy2QTnOsm8A/jPaCRoQCf1LIC+YM1t3V5n8rHpd9bY9kbgNIQLsJoktnV4d/ZQdIHN3dXf634gEaMySyl1/2Vju2aO/s6Fn/d2/F9l+f/7x/t6fn8ccf79FJomfDPzaY70jv7k6a62xobyetDFrf5LT7W/a8DLzxxnYjtdqivT037QoBVmAM/sG4sXu3/8UCne0cft6+dXtPy1v2PNROWhpg3GDQh9UvIk2T2DewlYAAlrfIWJwgbiggAbGO3TNmeIBhGRDo2m2BTW5Csxvp8NDDjzCrsqf/9qxUDK+SESOqzDmNyy+/XN536PvMc+985zvlgANGyeK77jTfM8HgHcBzt0DIqyRNoQ8PJHNQhxQOliT5Gi+8hOYyRcFeniXSLNNSBWVlEBtCGZ8jjRrY7GU0BixcsDloi3SSw/TlDlQyHKsSxnLYIMNMtSjESnSos1c7uEpmyvDrb0ROPXqqvPTSP+XWny+Sm29eKM3Nb8g137rKf8g7dTzvWwuktATBZ7KAdPIT7hYo9JFSjvfpUs45A6ZpKWMycNKcQPaseuEEMsO01IkRLK0ALQ9lXFUBkpFPpCGM5QALgExmi1iCM4C3JDkma5AyKbpakmkpDvYxTEtjDk/uDdPnvLPOk/PPP18qK0f7dzyMGTNGLr/0Apl99mz/Tl/QTCeVOgzTUngJZXRCVnAbWNdRVqiJKsPTtnCFs2fAMil2cPKcMXSQJjmaRE9hQs3H/8wLSAmMQmOwYwTNYIW9xDkDhgREWVIrMIAzJkuoiRhlgtsNCkgbv6iVLYLBkkFnltoKywu4SrAFHLoxBl+a+pSkJmK0FYBNeph328KNkVY8KrQx2ovhgReINhnoUyw1UYJBSILeD4C6gNWhGY1qYiAzjpbHSPVKMHQgCizPCfzKcMCHdsJZGgZ9WEKSuNVKH/u6UfqWwnFgbUUQoVlqENJgZ1BC0BO5JDWRw3Hkp7OBf2GHSEMYawMZKwNGcBuWmggSkOjS2hZoUEajGtUOYUnsSQr2TB8jrgwoEhAhD8CsCAl5gcyMoE+u40XeswXLUZ0XBY7g4gAGCIxxI87ZK2LFQGasLgAcrGTwIUuNH6kokIBIainNzL5hWWoigBEDmaWzY+j5AS8mgj3D0qhMWsnR1DIKLNGtQRrsEk6lf2UH6KAZQokX74EwAGu7UyZddxCFzoY02mb24BiwpJU4jPZiqakjNRXNSoE02OVyVFcocsVALhRuimdaSrGYwfKcYC3jsFYGCopUT7ImghrEZUTc01wYg5Rb2uJf2YIjacK2iXVwkVEeHDJlyFsoSyqL6/hCwRoPTT8l1ItVnkhNBSsOlpqIoQYpNgZyJmDDkSJYBqBBGUzPoo/RRRKk6LQuLhgyB81qghV71m1S6hDog1wInZllTcRSF0B9GqeYOHNWTjRBS/OJEwRJGh8qGHWDFRkD0YYwbVQG0xtrGcI5A8ahMzQCJCBGeVhgxUAOO3mzAeyyGcMLzWqCUCcgyRihFKzlOeewgg4KsT1OD22AFTMFLDURhQsxWWp7UdREpD0DklqPFRY0Wi5KRE7/adXK599AfnLVKlm5cqXsbN7p3+kPxp4BmNSzN7cHT5fNiYEMXSTDHI/DYjxQzB2BRBVlIGe1u0PylbSvmZayBjtMcgwYt/GYEKxB2jMgCUksRCoKGpSxMkhKiWGQXLjhmoVywkknGTcFJxxzgn83CygN6k0GKgb534oHBhZGo7JiILNMS9OsQ2ckEzpGHgArxq9xqU7oF207mv0rOzhpzklmlmkpZZNewYrxi1VBnuEnMlh8yOoXrHaPNITBWoaxMoBmNJfXUgSWufuB38obr78hnd3dMvn9k+TuxXf7qX3BMC1FIyCak+PYDwvIi9GoZoOdoatNk7xOsryWkmLhsqSoFrcHLe9/Kx6YCCj9Ygxnz0Cc4f6FHZJuM4d/FBQhiRFoR2HcUVCMyEhqNO0XDGGC1e79gts0Nva3eU6lUhKP2w/AXseBZUDuvMrLy2Xrjq3ypfMvkhu/8y2pGdc/Du7V110v37v2ehO5yAbJZJvWy97m3HVTmocXxMMG0GWDMramqt4BJnuVQVNjk1SPrva/FY+62k2yX2WljBg9wr9THFJuWuKIBmMJ0DmBbCz1xygP9jFsO3TbjjZJx9MybNgw/05xAB/m61tRwaIPqzys8aetrc2oioK45MWCVS/WuJGrPKNH93X3MhD6TQbr1683n90qnZeUeDMgrl1lEEe5Hvc6OzultLTU3AdwL3g+nBbcD54BMn8TXAd49NFH5YorrpAZM2fIr+74lWzdutVP2YMFixbJ/Dlz/G8eMt8LhMsQ/sxMAzKv89UjuFcsHaLknS9toPeinbLdD78TyJbWpt/hJs6s3/z7uHb8Z7P9BsiVhu/r1qyTqjFVUjOmxjyb67lwWuZnkAY+DP8GnwCuM/MLp4XvBbycmZbv9wPlHVxHLUP4E2jtbJWK0j17B9l+H6UMQLa0zN/nS8ukT5Q65cobyGwzINvvMtMyPzPTgHB6vvoBoDEAOoefiVK/8Ge4Pvmey0zL955CyxBOC1/jM8CUKfljuWei32SQDR3JTikjBKVOqiAPtUy+WRWBTjCD3/Td6+WgsWPlG5fN81P24Jtz58iNCxf534pHS1uzDEtUWEvicG/ACJgC+sRiXSoF2Sk2UZ54XOtlKXFsUol+3MT+K7NCsHbNGql7tV5mfvQUqaqyWxmw+LCtrdXks6+0e2NDg9E5FSrJZWKfo0+q05io2vJhW0enlJfZ16tpW5MknIRUjLBrs2Qype1uvzJg0YfV7tGKQbImyueoDm5YGzY1SEVFhekUX/vGPGncvMNP7YsUR51J0Rsb7OZYTYA+HCsOZVTGRrRjV5bm5p3y79pXZXjlcOuJwIBkOOA4gzgb7JoHo1+IDlD7FBj7VkTAhT4FMYdiFEGzamPxM6k8kSYDzFyWQoIBNkhzOdOC3usjH/2I/03ksRWPSGxY9uI5laRDOixHdYNJPkby0KcQmGD+jMHOsuP8u/Y1ER1XDqre379jB8aEC8BwgAFssjImg2QLxxokLiRHdfqXcgkHq7BhS2gzxI1gwHgtZVgTGZ9mBJCsibB3xUCkIYwWA1m7YS5HdVhuv/+498sZnzhNLr54jtz+izvl0gsv8lP7wn2Lc0jHRF4jmb+xkGQwGsmayNZRXXPLNunWv0PeWUORXRgTrgGsmwj0QUdmOKpjWRMxHdVBzWgNmHIS2gzxORgwbsK77dU7NGsi9FMGT1tu9AeIVJRYCXHAzONf5jd3/UZ+9atfy3evWyhrnnxCxhw0xk/534Hr9mhj2E90Rl1AmOKNOwpCw+JUNWXFY4HGndtkR9ObcsTkiTK0gjPYMdoK8ByxEeijbUVRE7UyMvH4kIU0ISQYvOcyJF+aWkZBqRdBkABYcQhYarRIkwGF4RXGjn4AVAwfLhVVsP/P3fGZjurMAGwJwxyEI+GGPgRnbCYMHqFeNsFttr6yWRIlCZk8+WhkpEtZeyZixIcGsPHLandG33CTOcJ8FgqSIz9WOFgM4gz1MssRWzwWp4S9jDKORQHow5gPWGq0aCsDbVEG05sOSFjKugTPg0BCl8OshmWpMChLYugiGVKixZ5BQ+N2GXmIv1egEnScsOKhqYlIYR2RB2OwcxKcE8gsB2otpk8wzmgrjQiDHUtNhHNJDsEKiCFIGGifYPB0TDjqwWiTgQ6ZDGDgpTiqY51ANsfuCSeQGQOvAkxGiXTmdlLKhAM6xbT8htp10t7cKuMnjvdukKwmWHQGfRig9AulDccdoIIw4QLeXtqAFucDQ8tD0YQQfRMx1ERumuQeg9UvOOSJNhlQB7t9JAYyZmSsDCh1IzWqAWMTEBIHYaAqxmtpe3un1K7/t1QcMFxGjzjAu0kapFhCCWvPgMI7oE0FiX9IfIi9NIo3Xy0PQ/JNCWevCF5LGVHKYqTwoixHfqx+EW0ycHEi0f9iAbO8Yug1SYMLVgYMt8hgeAbTG5UVo0P/Bx3VvfLKq9Kqf/sfEDpApXViMD1LAmKZlsKUk6E+TTZw1A5xbXfKHgZrg51kOhl3d/lXBBBiILMGX1gyMsZVtDsDkYYw1p5BUiqVAvaSLyIf2QJMaryWMnSjOjnR9lQIEx0rBnIxHl2bmraI0+nI+Hcc4t9RaJ0oulFCHgYk01KYclJMSys5YS9RHo7QhkwIfSzFcVAIR2yU/qV8yNh+oEyUAGncYJkUR2sqlewYTOZpRwmiAmPA1Jp7Nv2E/QdtUdZAxYg9y4qBXOg5g127dsnWrdtlfM34vieOGasdBZbVtp0H86TnotkeaHNGZ066rLCXJLD2VBiDBkCa5FhqIooqFyCNqyxEGsLMwElYyULiYGyQppMEqReAdQGkcUuAPozJAOdQyxg2w2AyQr1SBXqFfe21N6RH/2qmvte/swcMdYExmbXsPGYATzbRlvqMyaCigmSqSDLBZJmWOulBnHannS9JaNsTVjysGMgKBv/s1RjIWBZxZrA2zWnfWBkYsEwMtUoMpk/oX64T2gWBZFoKV7+F8Oq2hi1SvX+1jE5kqD1I7UWTokjtDjDK1NnJKQvDxBB8zDItdbU8DCGJZTK7r5mWsg5R7t0YyLTlTDnFmogVA9k7Z8DgVtLAwmKy/0AM5IaGBmlsaZSJ4yb6d0Iwy3P/2gKsWK9eWEf7NmNNKDQonW2BdsJ5cYppKQm0iVv76b5kWsoKe7lXYyBjGcJQEyGso5sm6MQJSz3TCE61zqqEvHToZawMvA1kAn2cIVomewYpxJro2SeeNe8cU5PFhQjJqqSMYe6ocF1WmECOkERzVEeyJmpLNlu7UTcgtTsrrKPZM2BUK2Yv0BrsY/TpF88AelkXMUexSYKBST/TnWklopY6kID9+0YSwb3gEwjf08qazSj9DrvltmS7JHqGiDOkx9MDBhsx4d8DQf5AOE3vx3Rl8c35V8qCmxdq44aWjxnPDZS3KU/bTl02DtNrHTjDz+E6VPZ+aRnvcTt1UCjN81xwnfkZTlMkU0mJ7x4i8aGOt4IK6oFPlAVlCr4H9QulgTaQfMBg3mSXpw4D1A9Oveo3viYHThgjJYGUGH4uVIampu3yxCNPyahx+8vxx5+gj+kEa/IYotftIl0lki7p1hVd6J1AkN9A5fHrnWp3BVkE3/s8B4TpEk4L3ceE1ZHqkEQwig9Ah36fgOYHWqfaO0RKK5R//HcC4ecj1Alo3rZDJ15HRlSpTD7Qb3KkYWM0lWqTOFRgoDnSAt7Idh3QLyiHfw01brJZGahit9cv/Px73xWiZa77oLHhw66Y9nW9rX+9zwW/yfzMTPPrinqhX5Qlhu/p7+Hf5CoPkJHW3Nymk3eZVFcN6auOLSA/0AfxA+KJoXmfy5rm3w/Tp3dcDT8XXOMz3OZZ0sCHZtzQ8qBsGDccfw+hUEGl32SAgSRztkomd0p5+Yh+Ukcvr6A+GE/1EwXAc8H34BPwwjrq0shRQhYJ5D93zhxZsHBRn7wLRiwtnTs7ZMhwhJ3z9IiZZcYnkFmPTKRSfb08ZuYTpgmQLQ1g0AeA+2EwHPw7Be/EZ7gMwfuDMuATCMqGf3V1G2X8+Al90rLhmbVrZPurW+WwY6bI2JqxZhAxzyrDYomfclslofQJ8gZwnY1XgrTwPXwCoHNZWUUvvYqFtzIoMdJvrvdma7NMBO0eLmOhdcL1zm2NutT3whQGafgXbhcg+G2u645WpfNQe0sprAzKwc/BAFQkAvrko0kUermpdnHixfcJ5IN/COlbVpaQIUojuEcJvyP4DJ7HdWbZAoT7e+bvs+WT7R4A77CwbMt8rhB6AanWXRKv8OIg437wfKHo9zNkhBeG/wWDZf/7e54PPoPnMu+bf/rX53sR/wDsGeDaKi/98aBSnLT08sK/IL/wZ+a9bP/CzwXfw59A5nOZafgHaTVw7mXzDyds485gcx28M3hP+Hu4DMH94Blzz2ePcFrmv93SKVtebZDykeUyblxNrzRpfqMP4Bnvjvd8OK/wvcy0zE/8CxB8L/afOWHrT5T4nu29wXvCaZn/cB8IpwNBWvAZvg5/BtfYmQmeA4L04Dr4Fzyf69oZoqtuvbb9B/6BsJQtrZB/QdmA8PdwufOlBZ+2fQL5mPf4kxv6WeY7gs/wNZA1Leb1rXBa5udA9/AvM//gM9v9XGnmemh8z7XeLxaRfko1pSIo7RjuKACY0NnvGHiwaYQAjtuiDWov2WFlwKhXlHMGr9S+qoOZK0cfPdm/kx2BFGMDFh9iZcDarEcHtEYpR+crJKsSeHVlmJYCkGJtEYvZ9wnA7Bmk7fJCPzdqLxIY9DEqIwIiDWEw7WIU2nTAQJdmAYajOqBFJURGThjoGINdm5RrPvYdGrp6rMJs4UbYQG7e1SQj9hshlZX54/cyJkuWiaHjKJ0J9AEo/aKVdM6ANEaVJ+BSmyMmMdo9nfYC2dsC+2DpmH1eNEsrXakw6OOmObwcuSgMCcicQCZYhDBWBqbjYHOGADQoo1GNt0iC1IETyIxDVQNVqctNyqbXNsu48b530lyw1D0HgNqKIkmRwBp80S8Y6N3wtQTWKYGK0ArEdmeBkxdHGGVJ9Hs1uA2JxxTl2pntJV9GcBvUqVJXKgz5hzVAeSsnQmb+xq0tBjItfaWuXoZ0DpExBw0Q4xjlYQycMej6/WsLsByxgYcoaqJqjhqEFQuX1S+Y7c4Agtu4FI/H9toNAxVGGfRxCC5sgGiTgf6x1EQM3yBuh39hiTZ3sJbJvjdjQGA0Khz55YvwFhUsCXGgPYOdTU1SedAwE786L0jLYUlzXAezHBSyVgbSxFKD+BeWQL8gyb6UMqUJZ5OAlE5OhOHHjIcM4HAogz6UuOmKSEVhxPcNkCaoiVhMj+U5Q53CAiZLxglt1IqBfK3e1NQsDa9vkbHjxvl38oCx2lGw+JDloBB8SBGSnH0rRrTjDOLwEElNRNu/8D9twSkN+heHnymrU0Uk+oDpGS+ELrIwbzfZEePst2mlSmmTAWOcosUz0DwY1jJOnpXBsxueNsw84H6BD8o4TtrjQT4M+gCMycAtZXkt5VkTMU7ms9RELFmUdgKZNIgDnHGDtPfpf+YFa7cajthShKU+Q02ERoBvohRBQkRerNUKRZqCLpKg/sq1Z7BzZ5M01zdLdeWIyG9h0IdlTcRqd4AilbVCjWZPIFY/ZTryY7Q7Te2pfYsSTpmkrmSpTxEjmiGURCoKpGfWngFjacRwVIdGgCTOWBmQeNXQhwEwB2Uy8D8zUVdbL8nSZORVAdOqhCKJa7szpDuWxCpOQvMi9AsCLwM0B44ksMrCqhGNNiT1aVoHIIZQEqlWrMGOZlrKimegYJqt2cKbnOzLA2alTHL+ZxgYsja/sUmqy6ulZnyE/QKAxPTBqVhbwJqIAVa/QFwNxsoAEjRjgkI4WMZkaXxTEcrDUstwckG/YPEzR0hi9a9IHAhpjLNJQTItreRsuLFMDEEfxsAAr66MDXajq2WsDLKoiTbV12l903LUtMnRmMcHY1BgrAoAmumkgtEvkm3QrdsTCKalDD5k0YdxgNIgzTEfNP6ICBVjxRxGP2W0116NgcyZCDDDJ/U/+80O9y2OOoVlYgj6UCQymJYyOhBLLZNlA7l5W7MMLxsuoytr/DsRQNKNMvIAcPKcYVKMNmdMUKwYyCz67GumpYiBzADLtJSml9B+weCfvWpaKjKEEs8AQSYZg13MsR95g8GbtVHGACZLnn7UnssyqdyWbJXXNr0qY8cf7N+JCNYyNsaJgWwcsRG6NGvwRc+ggCQE0ExLSWBoEwBajQgudYCYMiODh1jCeqSioDESBHNOI43F7NwzAyx3FJicKCZ0imBysQHNtFSXjYzJINO0dG3tvyU1yJXxUc4WZIBCH+VDW8ZH59vXHLG5pZzJIE06iUozLVVwVgYkB4VYGRBMSxm8DMCYhjNu7EXTUnRABtMbyZdhHkiQgFCn/7OmpW6nN7FYIrxn0Lprl+yorZPysnKJD3TiOAsY9GHRGIe8WJuAFKmsk3TojOXIL1FNMQFnqUFY9WKZljK8KARg8DTLtLRfcBtIBcFsFYsN0use6epMS8XQIcog3vIoc/CLpZOSxkkwnXnTCNaggywYofe+DxOJadBwkRJE5EJH8vIPXwPBezOvEeoTfe+qb14r19/4bfO7AHBvHDBN+L3h+0CQBvWQq9ewuwmsMEydUAdNRyg5N+YNGn3S/PqZZ2KoR4+OvSpxlHq/CfLO+ftceSug0zRshgkB0j3eg/dp+d1Yhf5Ov2vevTTBMxlpxs1zp14PiUs83aFpmqM+50nVKhb5bQirriCaWjgtuN+jZXhj0xty0LhRWk6RF56vlY2v1MqkCZPkvZMnaVvqusqJaxlT5h3xWI8ZQMwgi4aK6RJY/1CedHtrL32CevejZQR6eRuJCEaklxk0jpQfskS7p1okFh8GavV9V47f50pLdyr/DPH2Q0y7ZJY9V34K09ZK4x5nsGzftE2c8piMqN5P0wcZOkIyD7drFH7wIu6Vafpbve/KVZ6saZpvQB8njn2MlD6nf9pPXARcCvjD3Nud8z6AvNNdWh6wlZ931DIgH/AuviNv0BlBezD+oHxZ2zZf3gp8NjW9KQknIaVVI3ppZ96Vg3dTSvO4vtPUy09DPq7yfFyfyVqGjLbOVj8A96Vbc1b+6ZOW7xp5Y8xBDG//PfgEL0Hr4rmy2TPbDegmJgP9JoNswARRaMa5gGhevSEHiwQinS1ctMj/VjywD4Ki2Ep3LPqgPDC/LU/YFYhBY6ChoV7GjPE2ilesWCFtO9pk5uwPF1xXFn3akva0Afa1dm9paZTu7oRUV8N1dPFg8mEu+iAtm8o4230WH7LyaW5qFqeqVCp0QrBBLhoUCla9WP0Cc9bAUAlGy20NEDGQHGzAiGdgZma3yftiC6WPyY+ARIywwa40prRXm1ep1tZW2bFjh1SOrCxusCHRB5I8o16eYxQCSP2isxP5aOewhFlBEIBwjEYSzoJcg2DW+5DkCe3upjgbttgzSLd7krkdSPZEJPqw+kWkySCtbyJMYCYPBIK2BWMD2SzdSBtTrImAZU2EjalcnbkQOP5J71df26TXjkyfMd18/49BOw+DDxH2kkEfFqCsYCAmhDMqCqhsWWD0DVZbmQ1kgr6fdn5CwaEPp19EmwxipUaqtwVmL0ZYR0Y8AwDLaoYLCDCrmVwsoYtGzczeIiQBHTJBSnT9ebth8xtSs3+B5qRhQCIjMD3Dayl4EIcNKQNM+yBKJyxJcoQSlqM6HA6lyL7QZRPoY/bBCMB+gUvwXsA8dMagT0oIJlKKSEMYNjAYhWZZE7HiGSQSo83GkS0wRjEGOwA+zm2RTHMk35jjGlfVLS0tMmrcWP9uEYh5m6zW0HxsAT7GYUOKo7pSjvqiM9Gt9LGvG81RndukfZWTF6NfUA5iKlLplMQIunWSkkjb3P7cjIGumBmI1kWVURmTASRfhm8ihqM6wOhGGYbHhI4cAE6nGGCsDNCPn/jzX2RwWUJGHzDSu1kMVAJigKEbDQYn5MUApTO7SS2XfUawcGEMvjh/QxEmSL6JGKtlAC4/YBdkC8a+JwB1E6O7wxqKwYeRihLr5nQcb2VgT0jGngHACm5DUTkoGCqrAIwy1dfXa4mSMn7sISoMFD9psgYFdBxboQR5YM+AM1lyhACHIWkpUr7pozVoe2mcwY6lozcB8Rl7lgSBFmBENQSg3WCwULSmKmENvgmjz7aFM4xg16WodAZRlnyYlRlMz6IPJCnGQNXZ6qn0ag4u/MRxGKzOzIrx67ocayKWYQXrBDKFdxSIO0KZ6BBXg9BklNWFAjGQGY7qWMIfzvcw6sZq90hDGKsxIPlCn20LlqM6lsMyWNowlmks+jD2HbrcTmNOWj5ypFRUWe7Yk/YMKFKvwjOPtR8VMBFQ2r2TI9wEh0JtAfUpYwJn8CEQI7kcZzmqc9OclQGrX7DaPVpRtNAMpjcg6P8YewaY4FgOyyAhsgYqhn+ZtC4/baWXf298FbOTzJh2nPVyFg65GAIFSy3DioHM6hc4P8oASx0H01LGXpoxcSb0C5aOngXWygD9ggHKvqciUlOh8hym50hAjOA2YFKYljIGBeTFYHrQJziubgWV6m0Zdtu2RhldPbq4Q2YZwKBAUYuzTPocTgxkN6UtRmDp0iSpXsLR0bNMrgFKv2ANdpDECVmxTEvRLxjzAdRNDERqKhSYwfQ4+UmZDbVRGWA5LEOVSJO8tRRuAInVYuKFiqhpa5OUDyMd6FBQmp0xUSpYDgpZaiKYljKwr8VAhsTKoA+r3bF5nG63b3eGKhegSfQUSUvz8T/zg6YmgndGgk6cZVpK0kXSJieVxhjWVoDNJPfKptdksDNIRh90kH/HEkofymSAWlnyIcrBCutIEwAIAgnAEGwAB47QKPQhWRMRJibAmJU6BK0Cic4s+tDUTf5nXrCsJkxYR4Zpl2tPQQwqrPB+YA5Ge3iTAWGCsrQmqtu4UfYfOUqcBElZQDppKbEe63zQ+WjtHi+lCEksayKW+sLzEkDYU1FQ+kWaY/3FimdAO4FMsrbS2cC/sEOkURXLEArTQ3VBsGFmRDrDoMIK74cGZQx2CHvJcVQH+hQ33EFfnGxLyuixo8VNknZ5SCvLwJW5LdDuDCuydIpwMh+HzUjxDFhWJUm3mSP9arszJF9W2EsHK1SCep2lJsLeHmPcQCRKBiI1Feu0pgGBYVmHzgAcO7MFa7I0KwNCedICVVPh0xyounzpn2V3fLfUjD1EssVALgaYnCiDAgmsw4aAdWfWAYrm+oGUD1YGlLMhhFPVAOucCmvUYPEOS0jaqxvIDAdhASjHwVl7BvpH0R1ri7IGO1bowmIYdtPGjdKpf+MOHqcDwhAJRzqzAUP/DLA23OCbiLJBqjMBxYFjEW2VDbQJDspBQnhaDHYcNQhpsoSaiHDQgLbxSxKS4nFOefoFt2lpa/Yu4F89UaVrIv3eqY1RVaH3Or37NujWfODgC/nguqR1z3tyfQ+CUeA3ej1/7rWyYMHle+4DSEM5K/Sf/5y0audAuZFXtu9Ng/R7kZYK4bIh31L9F5TbBgF9grKC5vmuUV+o3pq1LOFrlKdArFtXK/W19TJ15jQZWV0pW+t3yJjxNXvoFZWumW1bZHkyAb//pcF7gvyBQq5RPpt2B5qVxtXabVBv1Cuoc5FobtTfJlypqrJUFwX8j/qhfMWWCfWzoU8AlIfQ7r352NK5uc14Li0FjWxgW6+gHiT6mH4B82S0OeCr4isLNAHNGukMSxfMWJjVsQzu6GjV2Uc7kyK4H57RgntAOC18H+hIIdSfymQIl5jxG7wn23c8F5QnyHf+1+fKgu8v7F1ihdNwL9tvgczvpl6JodIn7KUPXIfLE6QFn7gX3E+lPPqEn8v8Db4HyJUG+jgxhBAsNXUI6lfoNfYLIPliFYb7wfuC9+Aaz4bTulRqeuD3S3RdUiKzzvyYpg0xE0PNxBpdGeqP9F/wPBZ3Kc0AYRsNMr6H34VPeKoN6hS8L/wJhO+FyxZOw35GWdkeOgfPAcG9fNd4HtcIvyqxMok7ni8fPAOEnw3fB4K0IB00cbXd0fF66aDIlUf4PhCk4bOxscl8HnBAdW8Zw88EyJc36NCWbJey+NA+aZnPBb8HsqXhXzLp0SehK/DgfvBccI3PcDtlPoM0nGSGyin8TPg3wbMD5ZdMdUpZwtusx/0ovwmnBdi2rUkSZQkZXrGHh7L9LriXraxAhy4H4zqgB9/DvweC3wPhtMz7qFfcH7ij/AbITEP5MI4F/QIIP18Isv4ML0CGvYRUZsd1+D4+g3/mEf86nBa+b9KMUmZ3v7TgPdm+A0GeAdL+BjLuZ6bl+m2u7xgwcR2+35vmX2f+Bgjfl93eMi38XL/3+Nf50jztMSZL7z4+i7mGeWowEQCZ7wEy016v36JvTssJs07QNK8+gZpIx8w+z+MnCNcX5Jf5HQiuze/M8nzP/czPzHt93hVKC1Q7mc8BwT0g1zWex3ecQIYAEKThE/+C9Mz74bQAoAnaHS2W7bng2Wz3w2kGKiUGXkujlCEzDfcNQo7qcj0XXOdKA+C1FEIbkPlccA0E7832jEnTcSPfb/KlBZ/4Fwxy4TIO9BsgSAtgHNUlPTqHnw8+M+9lK2uAoCzh3wT/cqVl3g8P3lF+ky3N++6pvsLPFINIP4VOnKEbBRhOldJpjtkby2GZDObYCwOU/ZkiNu42b94kQ8uHSnV5tX9HsyHtGUB6ZlSL5ojNqdLhjsDQ2u5Bh7SCu4fmNmDRB2DsqRgT532o3RHI3lpFpGDtzSAfBn1QLwYiDWFgeM4JZAx2hENVRQx22cByWAYwGhVgnEAudJMs2ZyUnW/ulPE14/07Hpw0q9E7KZOl51OIgTZtdZZA4V/YIOHva1giRTjQCZhDZwwLHlK70xyx6Uqli5AVy1EdNqIZ9NmrJ5BxzJ3B9CzTSZY1EcthGUWKUhj6MOI96F8h0suaZ9dIMpWUd058h3/HAw7pMMCiD2v1hXaHGs0WrHqxVqiwTmEJJRSLGR18GeVhWe+gxbwzOHZg8A4AlTmFPqRGj1QrJ8Y5QWqOMBFO7zEc1Rk4HIdlGHgZA5WhD2EAxmZt1IGqualZ6nfUy0EjD5Ih/mZWAId1zkBrxuBXVixcZrsz+kVFBWcFBoduFD50Sij0cQghZQGaHb2umF3CGaVYjLNSodGHZerqf+YFSwIyICz5YgnOEp/lsAwDHWly1srZ0xrWO1FXBq/veEOq9G+/Mf311i5pz4Am2ZHUBbR2137BWDF3d3MmuTgpID6C2zBig7uC2M7+FxsQ+gTguklxGGMHaxAn0ccRghmwIlpRVFql6EalTaVWe30b4wQyBm+WwzKW+gJglAd5RJ3A//XiS8qUrkw45F3+nT1gnUCmOeSKOMHlA7PdWXtXrnGlbg+EvWTAxAZnOHEkqYkYYwZg3FHsQ2EvISQx6MMyqInGPUpEzh5FOUUnztgzwOAECZGxh8FcOTHKgzyiDJxbNm+TVColRx03RUqH9pdOadZEJJhaWRYJ7Y4NUgoYEismFBzMI4AxWQag6KG1bgwhgOWOwjiqI5xAhqjFAEtIYhnBRCoKy7QUXkspewYEr6UGTrUZYGyBTsjoO4Y+DGkTJn0RJqjN2zdKRXmF1GRYEfViHzMthdktQygxvncIEzja3bo8mFBKmvwvdmDQGMCGNkXAIbU7q14GJfYDJ2VVCZDow/KiGmkkBMMzTEvbdGXgMGZ50vKc5Z0RDcoYpFheXdPGWiZ/vXCad+vmFjlw/wP9O/0B01IKpUkmhpzVKbfdKVZ2pBjIHCkTdOZ4UUUMZEaZWDGQYVpKGX4YbuYB7RcMnt6rMZBZpqUYWhg738wYyIwlH9PFN2OyjDuD80p2qPsLGzZIKtUhEyZN8O/2B5bVlPHX6Gr9awvQInmxwFATKUhU1sGOs1GPGMgM1QNLncKKgcxyVMfYdzBQ/mGMGyxEGlVZpqWwpmbImvtaDGTEwmVJrYzJEqZ4+UwD4Uvp9bqtslv/Kio8n1PZwDItZa3kGCpGACeQWWoiRmdmxkBmgNUvAIoQQJrk4KTOJYwd3mRpD5ZpKcvkOtJkQNEfKmCyxggMwTItZcVAxkTAYHozgDNMb52heU0DN2/Zrm9KyqRJh/p3soNlWgpQ1AWkWLg0NZG2GEMI2BdjIDPoA8l332p3jmkpazxkmZayTIqjFUUlO85yZt8xLQVYMZAZE0EASl46oeTTsyJuATDunX1PHGeCwKcGLBM6hjUR4LsD9L8VD8qAqXBI+bDKw7KyY60IWYMvy7SUBpKakWVSHCkXzF4cNUi5UWFYg0REZixcynJYV05lhCWoYfgcDAIVQEtji1SOqsyrIgJipBjILNNARgxkgOX+ARMTpTykGMgsoQTnMCguF0jWMvtaDGQYaFBg9jD8awuw6BOpKEzfRAxrGUYMZDApXPUymB6xcCmNqiWixFfF8jyHlLh58xtSUjFYTph6nH8nN2gxkBUM+rguxxEbgoswpGiW4QArBjKDxoC3r0cQk0hWZKwYyAbd9moiFp3RTyn8Q6JPv+A2OITkzeYpI6nG9TPV2SWJ0lKPPdKDzAk8Y2ub7tZnYsbFLAYxqIDM5iU8byJNp2FYx+AZpCWTO8UZVCHOkLh5zkwM0JFjYzDQleNamSgzDe8z+cluuWr+5XL9gkVm8ESZjLUBwvSl282SEpKxCVij13GVJqE/R+fHd/gVQWB1qC6Sbrvej5kAE6Y84RVHuExY7gZpGfdRV7dT81H6gM2i0CFXmpvW6SnmDb/h58xBPX2voYFe96F3Rlp5rEtauuISL9ntbSyFyorBa8Ujj0pl5X5y7LFTfHro/2gbHWhBI/D5bv0+WPNq2LRVxkyoETflt0OWdjHIk4aydnRq+5VqCZXze+utb4rENyilpqMN010dJh8EAA/q3ed9mWUK7vllA5+gjknDH/40l6dt8/GDaRdtd1dvx7Uz9q5+cuURvg/47dGj/Ll90zaJD4vLiBEIbhPiwyy/yZYGAw+sBJNd2mNLUS/Qx9ezD1CGcBroAwsgd1ebxIaXGfv1PnQGcuUX3A/yURrHdmsfLFGO0jT0RwBtG6VOwX3EVeho134xdLhpO/TdAcsQIJQGGu3c+ZYJSlM6VHtqjudy5g0gDWNFqlkScbhvaVP6DM7+XJ7yYcwxY2jnLknrWIhnsNrIxv/hPpItDe2T7PToY8Zq7SflZdoPi0DWSGeZCCLp2AIH15xYuzhxu/iqc+fMkYWLFvnfigMmPES8wqDgxEOMUQSgekGkM1uJAfSJSbuJvmYDN9WuGQ1V5vJv+NjW1Cgr/7xKZnzkZDPwDIRNmzbJuHHj/G/FA/Tx3IXbAZG8yi1pAyCSF4wHbFU8qFcQycsGTY3NmKJk9OjR/p3iwOqnrtdRtV52UjSr3TuSXqQzWzRta9K+5cjw4XYnvj366Lhhyz9+pDP7cYND50jFYC2LcHDNSAaWcMotW0GBOoGIfSQEC7D0tWlIB5Yw0gNUchl48/WtojJ/pIkASKdIDa/gqBk5RDaDeBb6FAPbAQFwS1v8Kztg74qBNhPH216dAjDaHSsCBswGMkH7BfUyo92xUmCMra5w2j1SUVgDnZlRw8upIuF2+BeW8E5aErhDwWhUDFCUAzZmOdm/M9c3NMqB7zjY/xYFnE5olsYMpieYThpeTnDOGQAUnW8rpyyS4mzUlxtfSftOv2CZzKagutKVgS1YggT6BWeytB9TgchNxSi0OWEL3ZclGBvIASgbyFocBtMDlBPRKv1nOhpbV7tWWtpaZOKEHH6IsoC0aNJKcSYVhoSIdiI52aAJSVA5UODHLbZFGzZ+Cf2CxUDY92PA1InBi3nO8BQCrHQp4watf0UAmJ6xLIIjNrNBZglaDGTjjsK+YmhQjhoEKyf7jLCZGa4X1CKvrn9d7ziRVUQA9KssMAZO1uALerDanaIuaOF0ZsoqRcE6oQ1eZrRZyiWslhUs01KGqhuA40XGZLBXHdVRZi+FMVSExYklWCsDlgkda7Kk0SdDRbStsUU69e+QAQ6ZZSKVRKQDAkhqIhYfMjbbANbk5IzmjOLGGoUAxDNgubZg9AtWu5s9g26CEEA6EY1+wZjA96qjOhaMmigwwbMA6wQyKwYymJUxMJhzD4yVk/6FVSq1G1+UEv2rGTfGvxMNqBJD8GUtY1nwYiDblwntTpHGSecMWIf7jANHRhcjDXbGPJMAo4Il8CJD1W2AlcpeHYHzI1JRUGDs/TJAsSYq8y9sAV8lpM0gRqMaNwkM6Q5M5g92rVrHjjc7pHxUuRxQXZjpIs1RnYIxuDAccpnBCeZ8nDUPZbBjWROxHJbhPCsjmhfNERvpxG9cV8wMayLGvl6AfaVfAJGGMBSYEc/A04nvG9ZEphFIViXIi9GoLPpgsAvq9eaWRqMiOm7ywCeOM8GMdEaRgAi0gdqCFQMZoOwZkKyJWOoLqE8Z1KHF+GWpvyAkESpmDpoxQFKf7l1HdfsYGHsGaASWQy7KQEcEVHHBZFD3Yp0cdOBoqaou/KANYX7zoEzPAE2a1+GOkRdDADBgWROR4KlP9x2w1F+YDBi8yOJDlvp0rzqqYzE9OiGOUNuCZU1Ec8iloEhAWBkQ9KOwUgiwvWWHHDS2sL2CXpB4HkzP4KFYmqPSw6lh1l4RZWWQ5Gxo04SS0MrSFpR2J4wZgKONFSuxZ2qW9Y6hM4E+e9VRHZiMoRvFYAc/G7aIxTgHYuCzhiUhMho1KZWUDXaz/NR6rVixwkx2B+5fyEGzPSAJ9AaMgcqNcTZaWfEMAMoGqbNvxUCmOaojqUFYdv1Y6jK6V5K1ZtbxhyJMkBzVRW4qSqEBwqzKCIiPjkMLe8lgeAUmS4baCnXb0tgoLTtaZNTB+8vQoZwNpqKxj6mJWO3OGnzNQoUAVtwIlpUdSw3C2rAlNZfyIanDa79gCBMsNRqpVtEwkGkpDqThQFCyWQfFPCaWjBjI3moHnjr3KgnywpwzIHQg1G1zXb3m58r4cdFPHGeC1XlYgwILTJNiCoimpYwyYbKkrAxYYB6qYggmLLt+nblpPERApKKgwHvDtHTunG9LaekwKd2vVN757on+3f5gxEAGEOSExfIsKZFx6Ayd57Wtr5vLEQcU7wnz/6JpqQHRpPj/mmkp6mMcsbGkcUa7kza0sYGcTto3GKuvY8WzL/WLSJMBCvy/bVr63DPPyXPPr5aX//WyvPzKy/KhD54gC2+82U/NAEntAEd1jK1o0Icxw+ejTyHYuW2b9HT3yFEnHKdSXvG0+r9oWgqg3VkbpBT16T5kWor6ODr4MtSVrD0Dlmlp3IlTTEtZ5QEY9GGZlvaLZwAf25nL+s72tJQOH6pTqx2zdctuGdQ1WLLRckvjdmXm3TJ6zBjz/sYtO+S2234s1994rf/EHlz1zav1/nWG2WxUEEkVg+K7lUGG2E3PXZ1pGYKAGTbqkO6YdJd056RPIVjz5N8k2ZGS6TNO8O8Uh80NW2XsmFH+t+Jh4rXoSt+W8V0EOYEveks+ZLU7q180NagQkOiQ6ur9/DvFwe10xRlqr2rsVPoMIdAH5YkNsZ8QWO3e1PSmlJUlZOhQu1OrqXbln6H2E7gZNzD7ltjR2ZRneIVHn9CYWKjblX6Twdq1ayXZUi4V1V3S2amZJ6vFTTSahaPbVrnnfpGAeVeQf3e3J+mVlPTXCS5eco+MLK+Uj3zkI73PVVRU67tb5dobbpAF1y+Q5uZGUz6nvFmXt0qAAa7D73XblLkSTeJqeRw8A4R+k9xaI1U1W/fUNZQWpgOunXJvmY/flB/c4L2zAIAmLmig+Zlrv8ylVW2F0dr/zZo1a6RmTI1OrKOlVeta7iQEAV0SCU83jeuqqtGGfriXmRaUJ9narESvkkSx7R2qQ2+9ikRQTqBoPgy3od/uUds5Mw3X6BcVpRWFl8OHqdOg3abdlUBmrYK8QSsguM78zEwrLS3tU4Z+fBixTuG0IO+ioHmi3U0/0zwCXgvnmVn2bGn4BKDQQ1uFyxflOmhblKNN+bk8ozyZ7Znvus/YkdFXs9Uv4NegfmH+xfUgbXe0ABQ8SC8aWj5XyxeMYShDMJ5OmTLFfEZFpEhnqVSXxOP2SyOvvCktcO61Gmzk7/zlb+TuxXfJYyv+pM/2f++8+fPk5gU5VEgFINnWJPGyamvJBZveDOdniPfgxnokYRGkZK1OBHV19TJj1ilSXTXCv+sBtA3CD0I6DquQwmkB6mvrpWZijf+teLAiOrV1dBYd0i+MtjYvIth/ut0D9SIr0hnobMM7ATBoxZwybTM7ArHavaOjS9vLfvzZtq1Jeb5Mho+wi5aXTKa03YvXNwXtzho3Ukn76IhApGZCPFMGMBmYmKo50NneKZ/4xBlSu369PPiHP2SdCACWozpY71DM1kh7GCiPjXXTzuad8uqrr8vwqiqpHt7f9jg82GfuJWROBADpbJ9m5EkttkA83H0K2u6+QFYU9pCcs5ktpJOoAMvKDgOfLUyMZxYc+7HM1pSzt92Vfxj0oezvKHjcEwGIZ+Dk2fn+2mVfk1NmfEAW3bpIhmcZzAKwHNXBmojSgUiDHegDW/Fisf317coYroytGakrDPsJinW2zziGY5CZMXEr0O6U08za7hlzalFwq+yleQ+cBvOsifYd+qTEflUApLU8jFAENKs2LQ9jMsDqi4FIXZRRYMB1KnVlkF0/BmuiJfctkaamNrnmmmvMv0eWP+Kn9gUr7CV0dyy/7Qy0SbmV1LG5od587j9qjPKZfaPRrIncTgoPsXywOIlqnTIJblGwj8YgURPiB9iDZSFFc+RHknxZYR33xXgGDCEpleLwT7SiaKEpTO/mljYSZQm59Wc/kcMmT5KJR0w2n6NG7e+n9gXj0BmQlBIlgL0HQnRCBtPDDUCx0m9T807Z2dIs73nPFKmqOoDTgQirCwPSoBAnlcfbqrUHzWEZy1EdabI0h0OL5MM+IEm+yIcGQl4sFRrGHgp9SP0iUq2YTJ+LkO879H1y1qc+JZ8441Ny1qwzzOfhRxzhp/YFa88A9tQMaYrm58aiE27aWCfDy4bLEYfWKIF0ImCc2mR1Qs2HIQGFHfDZIJlstFLHscFSErHURJ6jOkKoSR2kGO2ebT+rGBivpa79iocSc0TBOjFOmbgVkYvC0P21tZE6IWkmNHsGJJD4tegB741X3pADxx2oDZVQJktROlCadQIZgwuBX1neGROJ0ZTyuDqMM1bMnSSvpSxvmt7KiaFc56wMOgirdwBml7GhhA1knMVigNQvUgSVMBBpxGAUGEiUV2te9jp6WgxkY9ZFkKZ0cmIMCmbTroiJrr6+Tjq7O+WgUb5pouZBYRDingFlsiR5Z2R5LYXumHEyXxIcnS8rFq4XA5nTLxjtnshjgVgQtEsQhh+a4IcQt4y8WCeiIxUFBebsGShzEDrhvhYDOa3EYTSqURMVGG5wV2urPPv0eqmoGt4b1hJ5MPSahCp5oK3kOJv9TG+1jH5hrJsYDESiM4SSGMFvAxyxMQRJlhWZyYVAI5aKMa1tTqEPY4ZTROJALIcZaiJgn4qBrMs0hgkd+jGjLwOFDnjbd2yVVv0bXzPOv+PlwagXS02EWLiU1SXJhA6HfRhCAMCYDCoqoNqzJ1BaOGoiBH1iWKhgEGeMGzRHbNpHGY7qWEIJ1Gj7FH38z7xwujmVNwMUYSlLMy0lxsJlDHaGPgUOeI11jeJ0OrLfqEr/jgK6SM3NFgynXgArFi7NpC9RpYxPWKEqjRmduVPbjwGWwzLsGbBs1ylCAEn9pQ1G4WmW4AdQxo29uTKwdaTEBs+0FGxvXzfGwNuLAhi/tbVVNu/YbFxGBCoiA9j1M8rEsiYiAaovhiROi31NmFAMXKhl7MvDOodB458Yx6SYRmcSWGoi5MOgD9RNDETKhbJfoPB04vYSByPSGZBwqijGeMw9g0IG4NdffV2G6t/RU6f5d3ywpDrWBjJWKgx5ItbDUVc61cr49g2GfkEpjwvDCnsCsaytsIdBqRdJDcKykoJpaYwQ9Y+lJoKun0EfjD8MROoRKDDnfa2GANYgSKxe31OmJ6wMQB/GYGfURAVscDXu3CbDDizHFNIXurqgSFMs01KSNRHj1DDAsiZy4tpi9lszSmaYXBMmJ1KMaMR7oAx4ysuMccMz9LAHaJxut1c1kgRxGn1Y5YmUTbp7CGUGY0mszLCXlI1E0nLYIKIUBKd+295olAljc0eEs0WMNRmQ6EOyKKZZE0EiY/SLhFOp9LEvD9OhG2UzGpI4YaBy4pyVAe3kMElNxFo50dRW/md+lHCWRfuaaSmculHKo4MCg+mNmkil6Ch48cUNUpoolf3HZnd7zND5stRENPqQZlxawHcFozMnXTgotCeQm+ZM3o4ziDNwFrDKzQc3xVkZgHsY9WKZcrJWBqzyZI1nAF/3GJRwKAu+3zFomrixiWqjysDGK/zoZH6a34buVer/LfotnGbyNT2oQrlOc0526hxRYu4F15WJhPfe0DVWFShHuX6fP2eOLFy0yCOklsuUT8o19/zX2C42A65At1qud5NmMxF5h+sABHUAwmnBfeRTrvkkUUu3Wco1Dy9XLZL/TOZvAuROw/K81XTGIH84r0P5e9+rq5ny8gpZtmyZVFaWy5SpU2V3W7M50IcAFyhDAn6J4AfKqdZvSkd9ldEDm/ZTGmd89wLaaMlB42STceDnKO3r6xpl/MSaXh7AHgvq6jgV5jn8Hu2ZmWbo7NcjqBOkca8dUBOv7rnoEL4PhOuO/NF+Yfp4OeJ5UL9/WrhdetPcwaZ8XvoeGme7Rn08uno81Jsf5u1S3A1qVWAZ/LSmZCOaSapHj9Y6BvwJeHkBwW8MHXJdY6WrbZjrveGy5UrDJ/qFJJWnE1UmDXkHz0W57q1fq74H3VxTkQ7gE+8OgOtsaeH7udq9kDZr0nvS3KlXCSmpAo0yyqr/e78fmF5t2vCVyjvo+x6fa3/AOKLANdyd4JR7trTgnnmmp8ooS1BalAHvCb8X5Q5oh79caXvoo9AxNdM9fVQMvgbuQUNAQIqY8tSgQYOlWz/RiXd3pSVePlwSOqnulh5JDPZ8l8QHxWTQ4IQMTid1khuqKek+ad2aFte75pnYIJXoU5r3EHGGlMqQWJdKMrslUTJEBunMhhl7SElcBuvz3d1ekI7w9SDNc3CPDnI6vT/+58dk2sknezOivmfwYKghOrQMupzUJVMPNtJiJdIzWL+n280MjPr0DNbSaBoO1JQMFunauUtiQ8tlsLZIuA4xrUM39iX0vtbQ5I/fIM3VNNzD71P6LuMQLqWEisd66453oaz4jfdeNKDSQa9zpfUM0gmgG2VwpETrEdOcunWejjuDlQVKlIZlJm9Hy7L9jUaprd0ok953mOxfWSWD4kMFIUN3D9KJYvAg6dCiDyop199oXfQPdMUzXjyAwf2/D6lUZhokjjZ8PF6p79E/rVJbc5vpOKVapjjiBqd1UI8PN+oIPGc+HW0zpRPaE/QrUfaMKZ0h6Jq6anl3d6UMfTBWgaaYInLRIfN+kIa6u7tdGRzH6nIP/TV3U29H29rwgP4uMw00SWnesUGODBkck127dN1U6tE5eA7vAb0Nv+uzMrjCtK15v7bNUM3T7Fkovw1Rfoa5rCt4n/Kw/gYhXZF/jz4HVyB928/rF/gNytknLTZY2jZ3iJTpgFOqy/0eWBYFNPHyQithXg3oEEd9UO7Qe/Cb3W5M4iXaZ7R8Qd2D9wZlC/hZqZkjTXmmXek5NCFpfSfSPP73JOs9vynR+4NNecLX4fqlS5QR9X7QZ1CncF+K0s/QZ103JUPiCVOGMO3S2scxhmS7RlnQ7q7mB76q1LzfauuQwaWDZITSOeCHfLwSbsveNKx2XO0f6HNKh5IS7RsxpQf6rKPjnPJE2dD9zNiUmeb1EQzUOpYNKZfdgyFNeDzXpWWHzyPT3mYsG6pP6USm9DR8N1jHSTzdo+OznwYexe93p7QNnJSp++608ljPbm0sTS9wZRYp0llHhxcZyhbYbHNi7eIoIW3AinTWogUapo3jNVDx6NAVDSYsMKsNQJ9YTBs1nluF0aVSyYP3/tHsm3zyk5/07/ZFSiddw8SW9aqrq5Px48f734oHK+JVssPjHctqUdsd9bItT1Nbk7itrn2ks2SXSqT2+mOsBKEVsK0X2h3Wg9b5JL3oiNZ03obIhgkZXmE3lqWSHRJP2J98RT/F5GdbL/BhWcJ+PzZS97TtxGEU6m4hG1impVBjMUxLse/AohGO8OfD9sYd4ja7Mm7CBP9Of0DiZ9QrkbDk0gCkjUQljnXHAZjtblSVlmhrgAKCAPct/8IONAeOEY0hBgIs/hjtDkmZcQJZxTX/yg4sXf9eNS3FZiTjfUbHBf2DJViO6ozeWP9sgfGbtLeplcvvlKt+02aRKpGRlaETxxlI6fqeUa9kG6lSpI0yiidNBavdUS/GIFWepy0LAsmRH/aCGIYVcMTGQL5QuYXAePNlWCLuY8FtaIKo/5kf0D8RgA0SyspgH7MmgtdAxmSAyRIlyoWuzrRs2b5ZJ4KRMmbMGP9uf0DnT+nMHAHIgMGwLmtwIbU7SyLTadf/tANL0sSOCMMDquFDQrsjHwaM9p8y+pJMXUkS5F73WkpZpinyDXZRgcM+FJiNK8KgoJ2QQR9MlvkY7bXXN8pgt0SOnjrZv5MdCWzWEyTfWIrQcQAVJih8r+3FACxBKPRR8jDmgxJOtXSg42TUlmw2un4GKJMBqSw4gcxQE6VJh+AwyTH6RSrFEQIiNRXsl1lqIoqjuhRHImM5qkODkib5vPTZ0rhNyivLpbIy/0YjVHGUSY7ljkJBEchIy/MWl0Ofnbs4OnqWozpG3wJgZkxZWcaGcMYNFbYo+UAtQ1jtYtOXApaaiCSpRyoK82QjA0pDa2DwhqtebE7ZgtGggJkscwBulxtfb5TxE/73ThxngjW/URpMgWW+LdDuMOUrdmXQ3LxT7rprsVz1rW/JD757I8KU+Sn/eXimwvaAJRFDT48VM6Vv6GqZtYHMAcP8APw8mCJEsgTRSE2FWZmlBqE4qiOsDMCkLKsSgMH0Zs8gnV1NtHzpn5V1BsuYg0b6d/LA2FnbN5hDtCZiMCzjBDLaKTjMVCiWL39QPvvZc2XZvUtl2vEnyvULfyiJqn6eoQpGsgWH/uxpzQp/iPC08ThHD00ZqNxd/oUdXHiHJVSL5TiPpV5mOSiMNIQxJV+XsNSPxe07IECzJtI8GExvTkHG+uv/du3apZRLSuV+w4zUNiBI6gKXoF81YC2HSXyIo8NR1SBrnlwjP7jlh3LeOWdJXV29LFq0SJY8vERmzJhu8mGoL2BN5BIyovVTp5wzsZDanWUlZdBtr+JhWEQaKH0Y/MOiT7SmIhUaKwPGUh/25gywrEoYeQDmMHoW0aW2tlbTEjI2FM1sIHDqRQLJGo3lkKv36H42aFmff/55ufPO2+Wrcy6RJ1atlJmzZspdi++RSy+d0/cQHqlfsHwTsfzjY6Oeoj7VwjDKw7Iiw54BzEttwervoA9jsmRZkUUrinYQynJGpVuKmRhhcAGTerpj+/JQOqAC6otM22x0hIbXG8TRxdA7xtf4d/PD6CIZ9fI/rWE6oX9tAZppqe8rJgDyfemfL8ktugL46lfnyVNPPSUTJ0+Wm264WS6/6iqZkOMU9r7mtZSmo8eKh7FnoH+M8rC8lhooL9qCJZRQxkLFXvVaigal+G1X6ZYzkNsv9bw6YVDg5MUY7KCygt+RMJqbO6Q71S2TJ06RIREZ2ZMU7OvlEGMgU0AwLTWSfMikuKWlUa6/6rvytcsuUVo3yc0Lr5WLLrpIph49VUoHCISCdqfspZW2+Fd2YJlglju7eQNMpBFmAOiYQRl/NJ99KgayYl8SkiI1FUxLExw1vTIHwSyLMKEAxlMnYQsZewYMps+2p1K/qU7KyspMaMvI0EmDsZTlUBn5dFPowzAtxeDtuN2yYsWTMn/eXLlq/k0yblKN3H//A3L99ddH25MJgaLzbQX/2BMIMZAZgwv2rhj9AhMKRb2cHkwZf+BUkWNa6l/YAv2U0S8YEokiUlEwsDAalaUmYsVABhh7GCwdYiawcnmt/jUZP6FAZ3GsE5LEcwYM2LQVpKfHHlklF3zpfLnmqmulsalBLr/yarn1Z4vkc587TyqKcF7GsNgycBI6iNv3C8RAZgwuUKNxzHg5aivG/gWQcj3HcNYg9S+WUMsQAIBITYUGpSyHhWRamuQYhCJeAqNDY6KkdEJsE8f2qFTW1P5bunq65MCRB/p3ogFxDRgU2tdiIBdjWorYHMtXLpfzzv9vue++X8rFX0csjIVy3nlfkKrhdlYYrD0Dlmkpy8TQxAZ3OQf8GO3OcGHTi5J9ZwOZ1S/2qmkpCsxaGVBMSxOE2V0B6x3GchjuMVj06TBO/72wlo21L0lVWZVUVVeZe1HhInA8YZKjhb2EKSdhsoyaB1YBjY2N8stf/Ea+ecnXpXZ9rXzhM5+T227/uUyeOFla2pqVD/2HLYDxm9HuLNNSngkmJic7N88GJDUIKwaysSYiqNfTOc4CFQztFxQND6nd+8UzgA/yPssXJWDXLleG+LyBiQH/wo2M62CGC6eF7wOp9kEyeOhuKdEE8H6u5zLzyMS8ud+W7y/6vubhWYXg+VzvDd8HetO0XqlmZfoKP2hG6DdAlPyC+26nK/GhXqvmey5ArjTz2a3SZqkjdS/Vybp/bZBDJ02UiTlOHYd/15tfvFTc1lYxvqvA/H4a6A3GC34TvDeclon6TVulZtyo3kW6YQsn1msSB8NcYz5ovuhTobTgPWZTs1PbqcTz8Bm8M/wJhO9lKysA1tTqGSAteD7Alm1bZdWK1fLkM6vl0PcdIZMmvVOmnXiikkF/FDp7kdzZJonh+gKlz0DILB9g3qsF7O5MyeCSWJ+yhsvU7zehsgZp+Gxq2oE7Ul29n5cYQvB7IF/eKEOq3eOdfM8F94Fcael2HexK2zXPuLkfTsv1m/B9AN9New1BRy+MD4PvwWe+dg+eA8L3gXAewM6db0lcy1JR5cUiCH4Xfi5bGYJngjTQGf0922+CZwfMz++nsSGaqAjSgfBz4ftAZhry7mxPS+nQ4Md6w1djFRrxbMDgNqgMBt1CN9ayARYBsO0vtzzZOtcPe2kD1KvNTRqCFRsmLgB0+5CkLLMxQVeC8ixfvlwaWxrlzI+ep8zrZaxFNsj3GmN14at3bOtVV1tvwl6GETB3+DrzMwzPCoTDPwi6gpCfmYAqaP7F86WuoVamTJ4i119/lRYk945jmM7FAnVl9Avk0+S2mJCMo0PBbbLRciC0Je37FsCgD8DqF8iHwT9YLZYnqnv7U7EAfRCO1wbMfhHQpxieCSM052QHMqdtlCkShFgEDDUR6gWrEobCiWVNhINlCF/ZmkpJS1OL1Iys6cO4uBqoJcCjkM4paqIsxAkzW3Cd+RmG6TMqrYBRrRGS5KFGW7N2jfzwlp/KvK9+XaZ9+Hi544475Ds3Xq8Fyd9RoR60pQ/qCirb1gv5OH2PPRhko+VAMCFYCWD1i3B72SBFimNh4NjrieIEU2lmvwjG52J4JoxoQ1iaZ01EOcxCimcAqYVRHtaGEugDvPLiP6VkaIkcNX2q+V4oEP+VAs4+vQFjsuzuTMqa1WvlB99bKJdffYU01NbJjFNPlB/95Ecy+4zTjWQd5T0IIE6xaiO0u1nyJ+330YBAfWALHMZkuJrH4UcG4uluyvgT08GXcQLZBIkngdEvWO0erShKRNtZB/CsiYiWAZYwJnTK+LagrZxUonWVWetffk3eOU5XBQNIuLkAGjOOqLOsiWy8M2IFsHLlSrnl5h/I3CvmS0NDvXz0Y5+QH31/kZx13nk591PyAZMuxXSS0O4YDFxG51KwvJbCNkWHTe+LBWgnoknjDyYDBhi0AVheSxHvnIFIucCEztNx2SEhLZIkxC92hhU3SGbCxHpN25cHEiKjUbGH0d7sSntbuxw46iD/bjGIK+PbL61ZXkuLnZg2rK+Vk2edKrfdcptMfN875c6f3y5nnXOWvOe90X00ZQNclzPAMi2VJKc8LK+lAEXAYZkUu5wlKryWMhYGzBjIFCGbRJ9IIyEmHsYJwFxeOQuF+xZhZlIwNm8MVOJgTM7luhLY3FAn8eHxPpuJhQLmuwwVBryWMtYGkMKj0mfL5ga5Z/E9Mm/efHnw4SXygxtuMF5CZ848zWyUUQBTV0LNYFLMEJKcRLN/ZQdG+EMM3iyTa5pJMWH1HsAh7DcyYyBT1O97M+wlq9C5vHL+pwD7ZYrel0EcBdRWr732uoyfUIDriRygqDD0H0PwhelpPgkRE8Dy5Uvkm/O/KXf+8i6zaX7ZNy6Vq666So4+9lj/KW+gYoFBH9bKANvZDDBUgxi8saeC1aU1dNygtBnJtxVvz4AzOQVm2LZgtDsQqSg8pueodxzPTNgKZvwOOSyzAYJdMJi+vn6HtKZa5YCRNioiRRrDi73ImmYdOst17D7ZoquAJXLuf39Rlq58Wj5zzufkW9dcpauAM+SA6v4rI9hmU6DtzqAPOjJFTVTKOUFKixXstlHow3JQSBnAFWnlw9gAzgejYF+Lgcxq90iTAQ7YcITfNjMb2sLt8C8sgE5s3HERGJbhiA2nZtetXyNlg8qsVEQGWMkRJl6C0NKLgD5wKfHC8+vk+u/cKOedf4HsaNkuP7v1Vrlj4UKZPDn/ZjAr8Dcz9jWjXzidHCGJFdSoPFFFoQ/NQSGJEXECWdoZqyfOngH6KaNurBjRkYrCGMA9lOtcSDJ7JKANx8H3EeumTZtelUGdg2Tce9/t3ykenqWMvTRF802kTP/c2rWy+K475fwvnSd/f/Yfcs4XzjEBYy666MK+AWPygGU1wYp9jXoxwFITUVSeShasUxh58cAZfI0LawoPsTZsSTGQtU6MFWo0ysTSlJfBmoihb2NZExlrB0JHdMXeamLzli2i2cjo/ff37xSPtJngCB2IMBkgXsDcr14hV3/7WiktqZLbb/uJfOFLX5CaMWP9J6IjBusvBpLNlHbHgMmQyEqTHB001JW25cFYidjgHP7hWBPFYpwVDxAjbPjvazGQWf0i0mSABmUwPVQXOGFrC5Y1EU5aUjbd0nYOp9xUu+zcuk0qh1TKMN9vig28lZy99OKkPbuSQtHc1CzLlz8iX4WH0GtukeNOOkbuv//3Mvvs2VYWXG4Mij17eHEs7AEyM6zsOhOcwS6V7qYMLogNLkJQyZGsiViO4cwGctx+IPv/fQxkFlzSqUQWGPb4YHgbCaj2X6/K4O7BMuVjU6WEYAPvqeIIOl+zET0wsA+ACeCBZctl3vxL5dprb5DW9l1yna4Grl+0UM74xOkydKh9vViqCxjMMvLCXhrFtJRUL1Z0MiAthAEYgy9hZcBSy5gNZIK+n8WH/09aExnrFMJ8gBi/iMZkC1ZwG9agYMv0Da9ulndMeIc5Z8DYBPTcAHA6UD7Aw+39y5bJ/Llfk1tuuUUG9XTJtVcvkEW3LpSzPnWWDA/iBSj/MMCKnAW/RP8XTUuxYcsC44Q2b6+Rs2fACojPMi1luEQBWEJApBbH7MWRgFQGIhScFdym0hlEGRTcVHGDAga2xmSLNLc1S9UBVcb9BINZPUnBvgPli4GMgDHnfOKz8oclS+TbV98i1y+4Xk477RM54wYzJCBYXFEGX6dEW92eoVEnRnlYpqUJFQIo6lwSfTDYMejDMi3FSpdhWspaGQCM+XKvxkDGgMloVDAYQ+Jgqa1a3B5Kw4I2xTSqE3Pl2RWrZUj3EDlkbI3XkRl10zwY9XJDG8io3oa1G+Suu34pX7jwQqnfUC+XXn6p/MY/JJYXWh7GIMVqd5iWMkxv0eaMerFMS6HLpvRTt1vpQ+inCsZgxxAkAOObiGBaSgtug35KGQ45/SJaUUhqIoCyYUtSE7G8lhbL8PX1DdLU1iSHjD9EhoBRXc7GOG0ZqwJZ7YZaufOXv5CLdAJY8cRKmTR5svzyth/LRZdeJNOmTYvMzBSmJ0lkrlNF4UPW5MRSE7Hog36RZmySKn0YkwFLTQQW5KhmOCsVlvqUlU//SGdJSE2lKvG0msEJlhdu5yCRCgxWvk8ODFphj5qOLr2ypYXuGxURTKA6NZ+qCn1Rs4poVV56+Pe4zpaGTyTr3zXz58pVCxZ4Egz8liA9x3tzldWUp0kngmqtPp7B+/De4Nngd5lpGXk7iWpxm5v1kVLPd04BZViz+mlJtiRl4lET5eAxo2U3XBmHnwv/LmqdcHq0u0rcUn02eA6fUevn329u2iFzlc5bd7TJ7Bkn6eB/qa7rSsxBPey1YP8nkLCx4jPO38Ll0zxhi4Tn4K/fKW01QWh63w8MUIbeZ5CXvsv8Hs8F7wnTBAj/Lh+9MvMP3pmrDEDoO2IEo384nbslWdJpLKR6QzOGfxexzZoadoirhB1TVd6fjll+Y5DxHtMX0L9wL89zvfeBLGkBD/V5b6488uQNGiWbm0wkQeSHQDmGZ3A/2WjGFccZ1Ntnenk3y/2s/DVQeYCMtOZW5VZNLy3N4MOIdUKaaWuULcyHA7w3nB/aCQjqGlznzC9LGYK0gA/dVr2nY2o4b6CysrDDq/0mg2zL3lSqVeJxe2sQdGbjqC421L8THZB6jLoq5srcr8+VBQvtIp1BUn2ro1nK4mXaKEOMBBNIr7jGSgi0wL0gLZeUUyx9Hrjvftk9dLfMOmmmDBlaofngHfa0NnGm0zFlXG/DNVwHIFf92ls7ZdkDf5atb74s//7XJjn06CPl07Nmy3DEYNZnzHN+O/QiltZ7niO6gD7BZwA31SxOXPNQhN+X+Rt8z7wGgmfQCRnOBU0+cG2hkms2OgDBdfDubEimdmk+dmZ9eH9jQ4O5OOCA0XnfNxBgouzEC+9bmWjTCbEcPGi58sFABTq76b75GBqrNBvmo176Z/KXgjX+7Ny5TfOJS1UVVob52zYfYDhh+KdIBHUM6jUQn+UCJkkIYwEfBrwbfBaKAcNeAh0drVJWZt8YmNWg17QhJDBv3tfl5pu/738rHgijWJYotda5FTNI1W+qlzV/WyMzTpou1b77CTeZ1DF8kDKI3SY7BgVMuFGq1draKk88sUJqa1+Tndu2yIRJE+X46dNl3Jgaqa+tl5qMsJfFAPQJmN4GyY52SZQRBjtiuzPCOjY1NmqnFms3JKx+mkxCao2bfzbAoAlLl7hj1/CsejVta5J4wpHhwz3BpFiw+JDVL1j0iVQM28IGSLoIbmM3EQCsSGflzm6aASaky0Kw481GqRpZ1TsRAJjlGWZisNiC1DAQ1qxeLZ/99Gflttv+R46a/AG58eaFct5555uJAEhiSUoCg4dYHm+Z7W47EQAlSfs+AbAclnlHDQl6epX+bScCIBYjCKIKY1rKaHhSpDNElLNZCQZgOXCM3FKFDnbZYJY1BF/gjBjIAKyJODmBYf2LCAAtN9e/LmMOOtC/44FFH+gYMbFkQ31dvQ7+P5QLzp8jK1atkquvu1oefvhhmTbjaP+JPUiUZc+jYGgnpPAP6XANq93RkRn16k4Q2lwRJ01xLCs71rkQqE4ZSOlMECMEbAo219etfV527mwy18XAuNBnCNokB46RigKmZ0hA2HhkOIZjrAzMjIzNGQKQV+RGVWlp5coV0tXZLe96xwT/Jhc4ZRnuzJgA7rzzdpk3d57cfc/dcsIJJ8ntdy6Sa771LTnyiCP9p/qDdSgGdWYwPas82JJkAHXi9AtOeRgeeAEWfWCxxWh3ljNJY9ZOsLwJHCaeefaZ8tSq1ea6KFjuyQTgON8DfSKAsZTxUK6Swr5h0gf6wSEXZdWoeUWVgBCvYEfdDhk9ZnS/A1qQ5hMx+w4NR3XYoIKTuNt+eLvMmfNlWb9+tXztsq/JN6/6phx66KH+k/nBUscBDH5lOQiDBVrmJmWxYBzGZB06K49xXBljH4SlRmO0e8rleDo2h84Imsa0ePsFcR2HrORJkpC0Vx3VMQoMQA1C8Q0S47AqHHIxpKBCVk6v/muz9FT1yMgDqv07ITguxQnWmtVPyvU3fkcuu+wqKSuLyY/u+JXceuvigjcoSYKLyYgxSPWab1oCZqoMoN0ZjupYh846ZAhlpaI9Q3sFRxBgCJK08QcM3RU9szvvuktX1Hf53zw0bGmQH/7oZsPP4yeOl0MOzh+DIy9I/WKvOqpDY1AKrfDcK1uCNErRHJYpfaIwPZ6pf/U1KdG/CRPe5d8NwcXUVHjvgVXC2mfWyre+dZWuAuZIXe0GufCC85WR75QvfOlLMtY2WI4tWBIQIQ8ANuusdrfuF0oblpqINYDvc2Evab6A8C96gWbOmCHf+c63ZMmS+8z31qZWOeMTZ8hg36X/hRdcKOPfW7y1HctR3d51R6H0Y0gc5gASYROQtWdgdvMJHQh5RWnURpUq2jva5X3HTZEhOdaX8AAaBV3tXfLM2iflW1ddI/PnXy21G1+UC86/QBYtWiTnKZNWjSBMAKzRV8HIiuWQq88hnv80dMBkrE4B8E5E9hkQjMmSJQSwIriZohQgSGIlfc/iu+Wz5/6XrF27Vo75wGEyonqkfPWrXzPpp8w8JWc/joKBYoNHBWc16NNnIKBBWY7qijlw1g/KZLbw6gR1AUNthdnZ/5IHb2xtkKHlQ+W9NXkiew3EXG7S2P9fdPml8uMf/kA+c9ZZ3gRw3hfkoLFj/Gc6KZYl6VQk9ogExsqSJQHh5CZrz4BSr9IW/8oOMC1lDL5mz4A0YTIGO5bJLEa7dLKwBjv2+Kky85QZcswxx0htXb3c8O3rVaLnmJZiHGMM5PAYwUAk1kGDUnSjLNNSmm8iHAfn7D9E6YRbtmyXg/c/2P/WH+ZsQA4pCBPXffcsli9deKncfs+dctqHPyZ33fU7mZglbjBOVOcyLS0EMWLYSwYYAx2QdJspki/6BUUqa+XQh+EeHjCuNggnmQHK5EQyKYYSoJgty5NnzDCfF1z633LE0UfoiEGaDBSUlRxp5RTpBDLrpCXrZOO8efPl5psX+N+KB/MkavgkYeOWRln/jzVSv3mH7GzaIkOHjpDyMkfaU91y3ufPkxE5TkCa1Vdsz1F3BIx58slV8tCjK6S6coRMOeb9ctrHZyr98qtLcPITlje29dpUVyfjIsYnzodM+hSLto5OpaO9FJRsa5JYYoT1gShWv2hshK26a30CmUYf7acx5R/bk/CpVErzQX/3bxSJVLJd4gn7yamYE8id7Z3y/invlzFjR8mKx/4i9y+9Vz720dNUOLbXKLDos1dPIGMpbFtgDxzT0nSKczKWZWII+gQDXW1trXz+v74oN9zyE1n2wL3y6F+fkqXLl8mv718qS5b9UTa+uN57MAtMjGhdOmKQuemaa+TUT39Snvrr32TBdTeaeAFnfOIT2g4ROqh2ZEa9aAHxFRwJkWNC520gEwqkoPSLJOmELYk+OIHM2J9hReDqIEVHLMa09Ps/u8F8PvrnlTJ16hT52mWX6zdOvUAfBv+wTK4j9QhGRwaMGiSkE7/x+uvl5uv7S/grV6407pExk2cD6wSyd+zeXk0ECRwTwsoVy2X+Nd/SO3smq3Jt7PC/K799k9xw0039JkVIIBtqG+UXd/5Wrpp/rew/brz86me3yrXfv16q4CiuAHhxpu0ZNlZkDOR+iO1bJnSsdscSP7Ne69auk7qNdf63vsDzL6x7oR9fu06j9jHGbDmconaAyTVlA1nBqFaC4GYeMPEMCjAtRfyOn3z/F3LrT35mvj/0wONS5pTJXXf93ny3BqlfIPY1A6RhPhoyrYm+9KUL5KYffE9uuOEa/47IY489Jh/60Idkuk4G1dls8RW0E8j4JEjQ6DgP/uEPcvVNt0jqTXR0R0447ii5+Ctz5KbrbpEzZ50rR00+Su8ndBZ3ZfXKFXL9jTdJl0oqGDx+/OMfy1cuvljWrlstRx01WRYuWihf+Nw5Mn78RC/OQRGgxLDFBpd/aQVIZAROY20ge+cVOIYDmairq5Njpx6tn//y7+zBqlWPyAkf+mC/PS8YVqQJozjrxC+gLeZf/ecR1cIuCqJaD4LXlixfIgtuXijTT55m7kEou//+30tT0zazercG+helg3EQec9ApMJ6Exk6cVQ+TIAFCxbIFVdcIQ8/fL/MnHmGvPfd75XGpkZpbm72n+iP+fPnm9/ZADNym5uUSpQl7Iu8CMA191lnnCE72tqkUrpl5plnyUUXXOSlKe0WL71XqsurZWTlKLn2hiv0vSZJVwoJ/ZeU6TNmm2AxgHHzbcshWi9sINtmU1dbL+NJXksZrqfbkq6UE3zLtCgjUto9R78457xzpLqiWhbd2tfN+hkfO0MmTpks11+/R/gBcFK8s9PeaymNPlqeynJdjRLosy+1O/bggEJX2pnAnkoi4cUisAHow9hzYtEn0vSPifl/y5roSxd8SU444QS58fofyB8feUTau9pVQl7rp2YHIyYqGgAnUVMECbFx0xbpSHZofp0SrzxALjj3Aj/FsyCq0L8Dx4ySSYdNkGFlHhNBZfTRD50ki5c80DsRmCUjYcmHU8yUQ1XEPQOGcBdjOPFTsNodyNaRL7/sCvnN3XcZdWeAm275oTz25Aq5/PLL/Dt70N1NMg0k0QeBViimtyQ1CKte8MJLcVTHWHUrWOdmWFZkWSOdAei8xm5ZG8Lt1EXj0IreRknp8qYM5ou+Li8WG6TPe9lkuwZjYXCKpZMek6nE0TtYQQ2i+Z1yyifkb8/+Tf744B/k+BNP1JGx0//dbn0PNpBSxkFUT6xErvz6PLl50Y+M3/5g2YfyBkvkcBnC94EgDQ2RTO6U+KDhki7plgS+6zIbmzGo156yp/ukdejyMah78MyS+5bK//z215qekNmnz5LPfeFcUz+U9YF7HpR/vLheO4WLA8Yyath+8sfHHzeTwYyZp+oK4oseDRTJjhYtzzCRIdjexMlUTQrK75RKOgWaKFVi0A234so8h/aIx8r0e9KkpdpVAiqNSzzdIW6sXO8pDXWl0NuptFwxHRD7pImm6bvatY0Q2AQqhzc2bZfRE3RlYOjsSFlssKFD5jVOvqKMqXSs9xoBTcweUazKlCeu5YHr36BdgHA75boO6ivSKslWnXArDlBaQqIaNHCd/LQ9ballQrnR7sqDaW0vPIv7mITBK8jXPOvzvjn9mpHm5ad80tkhsSF+HFs8p6tCXOLZm2+8RVeB18pfnnhCGjdvlrM/+1n59a9+LZ84a7Y+E7SvPq1t17zzTWQgVSMqDa9BBxzwXXAN3jM+epQhwtegMlx7o6zpTm3/ocOVPtiY7F+PMH1ypRkeTzYpS5YpjQaH6ttjytu+c7s8/ezzsmrl43L1ldfJ0OFKO//3aWzMoxxaJpNPe6eyrXJE8B7UEmOAPmdoqn+a2Ieupl/pX/g3Xr2q9RkdmzLqkbudvbTO1ibZvr1JtmzaKtt2bZNJ48fLu4880vA0LHmMYKll0B9oPsq7CMYD+mkuZpUeT+gIpLyo5R3sDDV9MKWTSqJMJ0y9Dr83QPh75jXGMrS96SMYV5V/gPCYmusa6FPHdJsWPWGeAR8YB5Vw1ePvyxaqYYisJuJEmNL/lIETWc4JfOTDJ8vKVX+Vp55+So4+sr875TAQ6Wzh9xf634qHZ+qqTFUYzfrhN79ZLL/97f8Y9c/X//vLcvIpM+Sppx6TNWs2yN/Xr5VPn3mGTD/xZBkzdqysXfOcXHHFV7XB4nLKzNPkG5d5pxkBSFFYOdkG/0kpM8cIfmoQgKdmHEFNpJ3Gtk4AIx8M1B0p7eRKHFv65CtPlwoz5571eXmx9kVpaNxiTopfdtmlfmpfNDU26/CQtA9uk+w0ptK2yOwXUK88/bcnZdWqJ/QdKTnuA1NUeDtVRlSN8B7IAdq4UWC7Y5Ctf32zNDRsljcbW2R3SZdU64o9UV4mEydNkCrL4DappApfhBUGq1+wTIr7j8rZoDMN4wSyZzrZ7n/bg1tuu0VWPPa4XHfddXLDtz1TrnxQoYUCbGhDyrQFNoUxEYxKiEqCT8nM2bNl6eKlcmjNe+XC879oAsZgIgDq6zcpU0IfO0Rn/L4VwWTA8FpqJgJI5ZZw7bVxHlRyYagLXB3EbQGJrFw4JpioVy7ATcE9S+6RLU075cSp03JOBIBLCm4DiZMB9AvzqYP5wgW3yWc//1lZfPev5BuXXyG33rpIzvnMeQNOBAZKg73d7jizsfgPi2Xt6mekfmu9rkhFZs46RabPmC41NWN1hWFPa6zAKcjDP4XAie9F01Ishxh7BkmpVGmjr57ssZWrZO7Fc+XKb19t9g/WPLNGrrkm/+aw2+FfWAIBpLGBY4vhVaOlTJeSLa4jL26slZ//6Ba5Y/FiKRtdJiNHjfKf8vDsP6Ay0qWyMkLNeG+C6AXJaylWF1g+2sKJqxjNQMxXpVgi0hmLCGAFb8FSfaDB7tKLLpApR03xv2WHk8htLFEYGGcDdKVSXy+Lf3OnXPq1uVJdXS7Xffs6Wbx4iV4XKFGnOcFbBmp3mGU//9wLsmzZMlm5YoWJaz7hyIky+8OzZZYKZhUINq8wkc70WVt4amsCSHsq6RTJ9Nb/zA9Sob0N5D0F39m8Uz73mbPk0ksvleuv+Y6RNhbfvViuvfYKWbgw94TAc0dRvBT+z3++JPcsvke+/tUL5aWXauXgd47zdIzSJb+5615Z/+xaaWtqk5oJ4/xfiPz0ttvl7+uf1WHIkZHlw+SkD37QT/HgMIgcgCB1MMwdAzCyYpmWQr+KgZwBTpMRJC1FsYe8QNfaDbVy112/lIvnXCz36qA6dsw4ue3HP5Lzzj/PuGAoCiTJNy39B7tdu3bJc888J0uXLpOlDy6V115/VUaOrjTnkz71yU/JkYcd0c9qyBw6K8YfRQbAPQzEZDBnsoxx6BypKGnleFv9KoCh0tto8/CL238h4ydMMI7WAsyYMUMW3rpQrr76Wv9Of6STHP2FMe0qcMkHs8RbbrpeLrj0Enm95XX5xhXfkv/+8n/Jlz73JZOeig2R9f/4m1w8/wr5y/onZOtrb8iaNWtkzpcvlt8uvVcwj2HSOPH4E7MGtwnTp2go0zMGuzR2vBnQ8jD4xyHowwGcPGeo0bC6YKyYmY7qCkVjY7NccMFXZO78ubJj6xb5/rUL5bJLL5cTTz6RshJjCAEYfwIkm5OyfOVyefzhx2XjKxvN/sb4d42XWafOkKlHTZMxNb6zxixIOAlxCWMHKxY3Jm8GfVIuZ3KKtIHM25jSDu2k9F/cuG04dupUWXLffXLyySf7T3jAYDnz5Jnm8M6NN17v392DefPnyc0Lbva/FQ/jg8VYTeSeE9FYqVSrrHv+H/LQQ4/IzsYGOfbEk2XmidPlgDEHmWcwqcSdUnlgyYNy5+/+RxnOG2iCs3GYAHAdLGhOOO7DcullF0lFRV8VlaFPrN3aSRjoB/nn/5pvIpYPFvikwsam7QSF8qBe+fK55hrvTEHwmQ0s30RRffi0qlT90PLH5O9/11Wqu0tOOeU0GXvQ2F6nhzTfTalO0y9s233Xzp3yVkeHMWjY8sYWGaJ/ZfuVyYTxE6RyWGXkcwPbtm1T+pRJ1XA7HkolO0w+tmDRhzU+R5sMIjB9FGCQdGM91jvoDGsiDPJvpZIyTCuVa9B8bMVKWb1qlWzasllm6Yrl5FNmyogR/RkPjYE6oVG3NDTKt75zjbz+2usqnasUAsselUQxGRw2YZJ86cv/LZPe9z7/l31h5pCQo7piAZNbuAq3bS+cph3PmAyU6R2VWm3Lw7KaaGlrlmE6GdhOlmh3dOZ82axS/gFOhLl0DjQpz2ARZn3oLA99utpT8ujjf5S6jZvkpX9tlNNnnS4f/siJWa19IEw4slvrZScB27b7tqZG2fTiJqnfvFkGlQySkfvtJ+PGjZf9aw6SiiIOxGEyKCsrVyHMTthi8SHLUV2yo10SZfaO/Pa6aWnCgfhrt7aeO3d+3j2FqMBJy/Ly0f0a46677pR7710qiXJHFi28VcaMyb30BIy6yT9JiBXt0rvuNfbVNQfXyJoNa6RK/06YdZLmM0BnT7ZIUgZb09rrzPamk4ibULMPnUCGxJooz+6ipCCAzk659Ulv1ItxMr9RyyPNnfaTga54ysv70/nZNetl/rXzpVLrfNHlF8j0aZ5L5lzI1S8KRbHt3qCT4xPL/iJOlaPrJVcqKytl+syZ1jsrjY1ar6pE74ZyschF50LBG1c5+URWEw0kAUUBa2Xwv6Emqquvk3XPrZO/PvakTDj0PXLCUcfJpMmHy5DSgddw4eVeQ32DPPH0E/LRk06SqgI7NyZLHBqJx+02uUx5cDjHssGgJhqrKwPLZqetDJLJlDK9/QYgVgblOiDYlofVLxobGqA/pZ4z2KR8uHrlY/LY6idlcs14OfHU6XL44UdEmgCNa/cye7VeIe3e3LxTtr76mjRs2yk732xSkWiwjDp4f7MSqBoxTOtlP9hhZQD+KcSFdTawJPF9rV9EVhMxdLVmMtCa20pkDDURnF/VbnxeXli3UdY/s0acEcPl5GNPlA+c8IF+G7sDAfTBzIzO89jKFVDWy8knTvdTo4M1WRq1lWM/GbDURNBlxxx7tRVPIuPE1WD1C9ahsxdf3CirV62U59c9L2NrDpIZKk0feej7Cl6JQ9L06GOnJsrX7lDTNjc3yfY3dsjmzZvlzZ1vilPiyP6HjJKJ4ybIAaMP8J/Udtd8ylnxDMoSMjxjr65QdGg/LSNYDrAkehYf7vWVQTo2yDpoRrErA0wATSodPPbYSlm/Zo3ER1TLiccfKyd9cEakFUAuBCuDLVsgja025m35rBpygTUZuOa0mL0u8v/iBrJnEMA5eY52l3Spdmj/RpFoamzUyaDwPQPUpWHTZnlo5UOyRT8TZWVy+uzZcuihh/pPFAdMutiIZm8ge7Rvlc2bXvcmgKYWiVfE5MBRh8jYCTUyesSeCSCMZCqpfcJ+8H17ZZAfkSYDnkSm/zmeKwAbzJ0zRxaGzFGjAAPS/LnXSkN9vYwZP8b83iXtYQT0Wb58KdTRMvvs2X5KYWDRx0gcujKwrdf/Ra+l2NNheatl9YvGlnqRzkRBkwF4ZfHi22TZ0hVmf+jWO26VqqpyCp2RN1jQfpDq65Vzzco18urWV70vivccNVmOGD/Z/5Yb+5rXUlZ5IPyBB23pzOLDSFO/rbohgLHtTtt75Ywa3AY+StasXSO3//R2mXPJ1+W4Ew6TO351hznXgBrBFYVLOIQC+mzZskVaWnSQOXg//26RYNBHl+apNMGtBfEEMgZhaxBoA1ZmeS1FXpR6dUZ3h7xmzZNyzTXfkgvOP00ly5jc+vNbZcnDS8xEErNUewVgxYhGuzdsrpcN65+VpXcvNe4hysvL5T2TJslpp30i0kQAxMS+3YEUnNLF7ceywDGeLVw4NrRcLQOs8TnyngHDtBQTYSzWZaUmwmnJqceeJOd84Ty55MIL+hGztbVV1tfVyT/+8rTUNbwkE2oOlRNOOi7r0hkzKpZX1iZ0KgE9/1ytbHqtTk48YZocNID1US6w1ESplGfOCi+vNvi/es4ABwfzmRRHBaNf1OtK9ayzTpNPnn6uzPvmXP9uX6x9Zq2JvbttS4Mce/x0mX366X106gHCG8g28PoFHB0WPrmgfzZu2yFbN22Whi1bpaunS4aUD5FDDjxYxk+YWJS+ntXuxcRAzgammiisRisWLFNXwWQwEDo73/KvLNHZ3NPZ3e1/yQ4kT50+veeOX/3Kv9MXCxZ+D5OX+XfHHT/z73pYt/ZvPWefe27P7JnTe5Y8uMS/mxvNzW/4V3YAfe5ZfE/PksUDvzMvlD6tnfnpEwUozwBkjoSXX3nJv7ID2pxRnu7OTq2b/8UGEfgwCpCHbXlmzZzVy88vv/Kyf9fDunXrei699NKe2WfO6nnqqbX+3dxg9VPUqRjyvLn9zZ5HH3y057d3/Nb0hd8u/m3PG2/Y9zFWvVAWRl7NFCYktlfrdv/KDnt1Axm6toSuDHKdsIVUMX/elXLLD26RX//6V/K5z53np3hp1y+4Tr577Q8lXuaIm0qqVObI3ff9Qeo31kn9pk3GUmDmjJNVesJRev+HeQAJiLFRBnNSuN5+73GHyaE13inOYjAQfaLCSBwM09LaehlH2DOAZBdYW9mAISEyN5BtVgZQL/3o+9+Xyy6/TGbMnCHrnlknow86QJY8+AfZsP6f8syaVZKWUvngCR+QE6ef2O+0ejZwVwbRVsxY9dX9a5M0v9khW7ZulsHOIHnHIe8ydRk2olyGl9lJ4QBrZbBNVwYJwsqAVZ59bQM50sqgvZ0zg0Gy6+pK+t/644brvqcrgp8bKel3v/21f7enJ9mxu+eDHzzB3P/IRz7Sc8lFl/b86o47eoZVVvY4jtNz2de+WpSk19nZSpFY//rXv/b86eGH/W/Fw0i+XR3+t+KBPBj1+vfLfSXVYoHy7N7tf7EAgw9RDq/du/w7xaPY8rz88os9OgEYfv7Jj27teUVXBFdfcXVPoqzc3PvkJ2f3dLQVzgfMfpqvP3V3dPe8sG59z6OPP95z9+K7e+5bfF/PX9c+rvzy757k7j2/Y/Ay0NrZ5l/ZYevW7T0tb9nTqL099xhWCLq0Xox+0drKafd+KwM4VQsDoeLg4CmMlmSLVCYqTRqA9OC5cFpwP0BmPpm/Hz9mjDiJcjnwwAPl1jvukCkTPSl72fKlctMNt5jry6+8Un736ztlzPj3ytmzZ8vFF18sY2pq5Pe//a1JD96Lk4uILobv5ZonLC6CtOAzXNbgXoDgOSCclu0+PD5WjhktVeUJ8y4geB8Q/j2QL+8Awf3gueAan1HoD+Aa94DgmQDB80A4Lbgf3MuWBoTvA7nSgusgLfyb8HO5fg8EaUE6ENwLnsN1Lt4LrsOfAK7D38O/Cd8HwmnBdTg92+/Cvwnf/+FNP1SeXiaVI0fJTF0VvPrvDTJq1EjlndHy69/92jzz6MOPijO6WhIIjhxCkF+2vIP8c/F1+DdArrTM54Lv5t/WpDQ2N0qbSrMjXe1nyvNjxlRJomq0OJ17YoO0Jdv6lCHoFxWlFdLcusdlN9KylSHzfoAgv4F+AwRp+Ddayxe8N9dzQDgtfB8I0oL0bL8Bwr8Lp2XeH6gPB9/Dz2RLw2cAfK+q8FY+U6bkd52eiX6TAdQxcK2KEHdxSemnvlCJCPcKsFLxfJRj+ZjSJ0wAN/McrDM8CwQsV7w0z9rdA7xoYkmp6yKJx+Dffoh5Hr/3/vQ6vdtsLg8aNMioic4669PmuReef17O+NSn5NVX/y37jRwpM048Xr7/o5/Ixz72MV36bZE/PvhHOfRwREfz7evFC68Z5B3cxztwhYEa95JJhAeMiwnvZ+7BcsHz+Ik8UPfgezgtfK9xS4OsemyVnHr6DCkdPsLUN0y78G+AbHkHn8a6qUukbGhp73PJNOqThsmAIEQfNoVTrqNlRrhLL8wk0kwdEb5Pr1Pt7aa94jGEKoxehiAN167sloa6N2Qs1EReUsFAPqB3ur3LBBnBOQ+YGma+a6DyBGkdyV1GredolUHjREz5Lo2O0J8u4TTjtti4L/bya2tq0sFrWCQ1SBgoE8J5xmNeeYJ+UUhMjLTbLn+4b5l848qvS0PDVpny/qPkZz9dJDt2tslnPnOWvNXSIj//n5/LFz53rj6t5Uu3e95I/X5nyqD/e3ztlQl1AkAfo44zf3vuR0XwG9eEvdQBRftq2u2W5qY3pKGxSV7f9LromkGGxofKuAmHyMGjaqSiqswrVzqp9B5kaGw872obdLm7ZEhsqLh6D/0CYS69voFrn2f9fonvaGeMI+BpfA/uB+2OWiEt3IeD3++hiXcvnGb6RKpVmps7lC8SUjFiuLkffkfwCQTXmTwZpJlDnQQTXrd9l/LPUCWVN16Yvh7TurhQ0Wn5lYagXcDv2dJQUxzKM/TR8RNtgXIbhCaJKNirewaeNdHA7hYwGdxww3XSMygmr/17sw707zOhJJ9c84zM//oceest7fBum4zcb5SseeZxGa+rhGLAcFi2evUqaWvpkJmzZvp3iocxO/a9utrg/6o1Eaw4sJ9iy4fGLhvWF2YSLR6oV5RBAQJWXe0r8uQzK2W9riI/cMwH5IhDD5dn1j4j//XF/5IpkyfLps31MuWw98sjDz6iE1VhnTgATvyCPrZ0Rr/Y3ZWWzXWbpV7LtXv3bikrK5ODxx8oY/eviWynz2p31gn2nU07lT6xfceaKCL/DARWv4g0GbAK7R2yQADs/oMdpMaXXnheHn30MZk3/3L57//+ssz/5lypGbsnOAywTlcJJ33wBBk+olqW/+khed+E4iYCwNZVLw6xLP/zcpk05XA5fOIk/27xYJmW0jaQWZMBa6OM1AlppqUqJMUk+wnkYAJYtXqlrFv3vBw/9ViZMGmiHHvsVP8JD3f95i75/Lmfl/cfc5Q88fhfC3aFEkZUF9a50LqrWWrhJXTHJkk3pyVRkZD3THyPjBo5qqiDWqx27+jo0smosFVcNuxrpqUsTwEsw4FIoyDlYI0Cy5ck1jYZwBwx56tfl6uvvELef9SR5t70acf2mwiAIw4/XJfT58trr7xiNREYONVKgOLFlqc3PC0l+veemkP8O3ZAZF5GDGSoRIJlrQ3SDqnhWcFtYqRwg8lmCn2gMsg2EcA75hlnnClXzb9YYq4jv7jzF3Le+ef3mwiA8z53niy+dbH85hd3WU0EQLFBTpq1vEt/t1SW3b9c/v3qy9LW0CbvO2KcfGL2J2TixInFn9gltXss/ZZ/ZQcT6cySxgax4uicCQgMDPrEhTBmKP5jpqWIWLTqb6vkD/fcJ1UHVMsklZpOP322MaFDIJBZp59uBv5s+Oa8r8uNN3/f/1Y8bNREO3c2ySOPrpCq8iqZPuME2sqJ4puIFM+AZVrKkhCNeofmqI7gm0hXzIG7hZ07t8mqlY/JX556WioT5TJt+skybdoxkfiiSVeobqt9cBuYGEIFG0Utg8OZW7e+Lo2bG6Vxu75f/w46cLSMGzteEtUJGVEOQckO+5rpJMs3EWulwqSP51jQv1Ekok0GJLta+Cl/sfYfsmzJQzKs1JEpHzhOTjxxmhxQXVgnYLmwtpkM1q5ZK3Wv1snUY6bK6DGjzGRpqxvFZJCKOVJmeWSexWQsNRFLl83iQ8ZeEdDQ0GA8u65e9aSWLSknn3yiHPX+owqWpFleSwekj5uULfqujbUvyrYdnpvokQfuZyaA/cYc0BswxpvkMLjYDXisPQOWEMBSE7H4cF/rF5H3DBhBPL54zjnSqR3wmmuukvE1xQ8yxTiqywbojot1WHbPsnukpK1EZs7+sPkedshVLKAuU5nNepVh9nj2MUd1DPqwHITZtHuA1ctXyw0/vEnGjKyU2crXM2cWb0BQjKO6bMhHn7oNdbJhwwYoaqVH/8YcPFrGH32EVCcq+ynMDB+yHCYSVswI1mRbFoDlqA4ry4RvKmuDfa1fRJqTYE5HcN8t316wUH75i59bTQRAVEd1A8LtLEp33NS8Uwa1DZKD33VwL7MTeNXAmEHaQlcpFJ04a89AYSv9AE66i7J/BUd1MBksBHhvw+bN8uMfL5LzzjlLnnxprVx73ZVyx+LFVhOBQQGO6vIh7EANJ62huoKTuEeWL5e1G9ZKp/696x3vkpM/PF2mTZsuo7NMBABMnG0t0Qx0lctor7SudBmAo7oYYdBMpweUnyOD0i+0XRmIVBRslDEadbTOyGn9s0U6iDRvCx00iwHCQcLU7uijcbZBAaZH77MENtgZ9MGgSdlA9j+tYWnCGQAdhzHpJpU24Oko+Nc//yU/ve2nctZpH5N7771XPvjBGXLX4nvkm3PnyuGHF3aoJxccRudSQJBA3GAcglz+0EOy4qGVUqu8ut9+I2XGR2bIOWefI0dPPTqaWpbgIRYbyJQ5JWavnweMsYiWyRas8rD6Bc4cMBBtMiB1QkhjDGsZJ87pPEVZlSRb5NVXX5H9xoa8RoLBCA1iDosQmNUlMaullmkPtE6EubJoa5l+iLByQhzgm665Ri697CIZWzNWljz8sFz2jW/IoYeGLNgIbQW4FUY/aAc3KWtWPyV/XfaEibu9q22XHDvtSDnz7DPl6GOPluoR0WNHuy422Ak8BDozmszd5V/YwVgTEaoFKyAKUB7COM4QRIFIRcG7GMKLMS0lLLHcFGdGhYqnUEm8rqlZduvfuIMP9u94YE2Wxa5W+gCnVSNKvvmg4wsNHAnRv7CFi/MB/ekDHe6aJ1fLN6+6Sq655ibZb/RY+fVvf5tXDUTpF52e+5BCgUGpflO9CRqz9IHlxqR11Pj9ZdpRU+X002ZLTZHqWFhaUQYY0Jkx2MU4ajRHJfF0t31HpfEhSY1mGzkyQLRqsZYzAI6qWyIWt2+NgNcLGTQ7W1tl7RNrZGjZ0L5LbVKjmslAO5AtsBxO64RlCxbPs/iHofoCsLke5NXa1GoCx2MCuOiiObKpvl4u+tIFJgDSly74Ql6VCqs8MOuMivAE8OCyh2Tt39YafzXvnDReTj4V5qwnyvjxE2WopT09RdjE4EvIhyHYAEbwI6zmaOddtCwMIRIeBxiI1N/TOtLRJF8CYnDWYQnM7pAEPe8e0fD6jq1Sqn8Hj+u7KnBTHPoYEFYG0Gm6Ys+wODBFgTI9Z3CxFyQAY8Whq9Tly5fLKZ8+XW6/86fyubPOkTvvvNO4TT9obLTgRBikKO1eiuOG+QFhA6qrJcsfkPV/Wy+1W2ulRAbJjA/PMCuXwydOluFDy/yn7eDqZAlfObZg9Qvjm4mAeCwuCHZmi1QBY8ZAoKwsCaePgUiTARqUUmijE7ffmHI7/AtbOJ4TqqjYsmmLtOrfQfv3jTIF+jAGOxp90p0UdnX3MWsiRrjB1atXy5IHV8j5518odZs2ynVXXil33fU7mTi5iDgUu3XSZZAojzURVgIv/uMf8tADD8jK5U8LjqkfOOFAmXHCDJk1e3ZfM0nSCsxxu7VX2DcYrV+kOZJvCjp6Qsdghb1kbUSzrK0itThMSykSELCPqImAhFOldYumTtm1a5c0bm+UMSPHyAEHHOTf3UcBSZygwohlcR3y/xowGOFw2B+WLJELL7jIhJCsGV8jt/7kJ3LpJV+T6dOnK28X2SkHc9wJYHMmFpotO9s75cUXX5DlK5bLPffeLxvrNulq9EA57qTj5PRPnyHHvv9YGZMltCpl9aWA7TvFfJKkJmK5f6BxM0vtqZMcRUiCSEsQSiIVBdIzRQICCJIvy7QU9tRRG+O1V+rFiTsybcZ0/84e8HTHJPMdZVaKnpWgjgMgATEGhahMj3fV1dfJPXffI5dedIlK/rdLxdDhsui2hTJ33lw5+tApMqTUXihBu+NAlDV0hdrR1tE7ASx9cKm8VLtRRlZVmhPus07/mBw55WhzKG1IvoGIoA8HTL/AoUVbQBInDHZwSc4ArIkYA3mMsB8HUM5yACpgM4SSaJOBPsV4mVGDEFYGDkc1qkwf3YSuruEVOWjsAVmHfQy8jMEuIS2cDq00ZkxQLEd1kIAY8OIh+F9yAK4dvvn1+TL/4i/L0397Wr7zne/IVVddLyefcrIM8fdjoBNP62rXFmh3xind9bXPyupVq+X5f2yQ5I6kjB45Wj7xyU/J0UdNlZpxNZF5lDW2oF9QbNdJpqXxmL2HUMDRtoqV2PM0S2gDP1PajGR6288dBXam0YDePzhAGiJuZ7u4OoaX6fIRahXcR0AYmInCVTL0mvhu0uATBydFQTKVCPEMAlIASROcBXr6mMkD0odZjmoe3oDao8QZpONhd780MYEzujX/wfKteVfIgoWL9L0I8qArDZRBn/Leq9TVAdV0IE0zJnIqDRgLgIzvyVYtTyneoR06U2rQPPE8Gmtb4+uy5um12jmxPD8ANdO3aFlUKsR7Up1dmk9cv2t5gjz83xvkyNsglOamk3voA5qFf1dIfoCmO2nt1M4wU2cnrjRKefUBUHb45gE5wmmmHbTFemI98samRhkzfqwXH0H/cpYHyEgL9KqxmPJMZ7PEhmhH1LZ104OVZ3r0cw+voK7htJS7W7NCHrtNe+JsCp5Puh2SiFdrmTG5pLyNRS0DeGnlisfk+ZdqZbOuCGbMOEUOP+JIGVczVtNUijNlG6ofnl/8ZMc2FcaHmYUPzmSAP70/rKi8OqUFfKd566epZ7i+/nW6S2mlg0tC8+xVN+aiUeg+yrut6U1p2rxF6t/YbJw2lu9XLhMOfY+M3f8QiQ+Py2AzWeH9gw2vpjT/hA6u2A8yA7X7lqTj5eY6hr6n7ed2dkh8aJmhXWZ7mvf6dQqQLQ3tnEy+KbH4MK9v99Ivf5363FegzTo6uyU+RN8CGvvtHLRZL/LkDf6MKYOG2x15RCoPoGm97an83t7aZupXUXWA5qWrH/0DMC4l/M2EoKxAn/v6LOqEAD4ppb3pp9iQRnky6j5QndBm4AGzwChBEJ200llbwu+caO+An8L3gSAN7RaMw6BzonS4prbpvZJeU1O8qhDsVUd18HnixDznTDaY+/W5svD7C/1vxSNKkBNMdMvufVhXI47MPPUj3iSTAUh3FB8sJPqwvJbWb9qkkml/N+KFAo7zGI78wt4r0S5r1/1datdvkPXPPS8nnDxVpk07OZJ/H6bX0kLaHe4hNm9qkLp/b5JB+ldWXi4Hjx8jI/TTcex9E/H6KegDR3V2u620fkGKH8AKiM/yosqiD6vdI3VPlmkXQDkdi5mXACyHkzqx50N9w2s4Kiej9xupnSN32RmqY4BBH0/a1ZnFEskOgh0eAInIciIAMAEAtXV1cv5558o3rrhaEjqQLvrFT+Wssz4XeTBFJ2TQB/CcC+YH4gUsX75UHn3gcfn3v1+R0pFVcsLMo+TUWZ5JaEUFyeTa0vV5ANCnEJPrfKD0C9YGsvIgBHJrkNQyAIM+rPE5UhfFkp9RaHRALP1twbImgnQ4EMvvbGgyn6Nq8tue20qZAOgTLFFt4KnL7AcYuPtlAeooG0Cqvvue38vFF8+RX/7iTrnwgkvk8YcfkHPOOUfpVhggjbH0vrnaHQcU6+pqZeWKlbL8LyvhxURGjttfjvnAUTLr5OkyunKPN9jubk5nZpkYol8Y1SwBFCGAsL8DeCpR+wKlHXsp3CAG1al/bYG4cPbkIheFMdgBRsdmifReMnmEuuWV11+VyspKOSiLKV8AMJntYAdggIJu0hZmX4SAWB71WUHQfIopEpyu/eKnd8r8OfPlpu9+T8bXjJNbFy2Qm29eIMdOO77oJXYSe1KkwS6M1l27pHb9enlsxWOydOky2fBsrdmEP/GDJ8rss2fLjBNPlrFjdRLIpCvh1DlAs05hgcQ/2EdiIJ25p1AkGAKtAUnDwbK2ipQLi8do1kTDSLv52KTOI1fWb3lDUx2ZMn1qXkKBPgwa0ayJCKeYATfGUaWgTgUJEypGL1/+oJz72S/Kls0NsgATwMKFcuzUo7RuhLaHlUvB64n+wGoZ9cLnhtp18sf7H5b1tbXy5o43Zfx7a8wEcPL0GXLQQfnPpbilHDqzHPkN1C8iQ9udIZfAoIABWBNJCUFPRFJbsaytjKEIAZGGMBSYoSZKSiVlVnXfIg1SORyWBWja0iTl5eXG7/tAYDSqsVJiHJFMcyRfmjsKlcai8M9L/3xJfvzjH8ppZ5wnGze9Kt+76Tq5ZsE1fqpWizBAoZ2w/oI1ki2aGrcbd9Erli+Xf67dKPuP3U/eNfk9ctJHP2TMQqOiWEd1mWAJbSz6AIwyseqV1sYnaGGVD+0FWiDmcg6dpR1SPAz/My9QYIaaCCsDhpqI4ZvIII8EjahIm1/bLOMnDez5kTERBGDQZ5+DSojZmB4TxAsvvCA/vPmHcvHF58ifHn1ITjllpjz48IPytUsulUMPP8J/kgeUA2qiYjdIt2zZIuufXSvLHlgma559Rmrra2W//UfKKbNmyPSTT5GjJx8h1VUj/KejoRBHdflAkeYVrtujAwNhlCKpiRjaBIBSJyJofZ2kbopEHWzgcFYGnk2tLWh7Brl0tUrcp599WifAmNSMPcS/mRssycWAoUYzbEaQoll0Dg8KStvaFzfKDd+9UebMOUf+8te/yimfmCm33rpYLrtsnozPF3OZxPQmJGhUyVffiQng2dVrzASw+q+rpaFxq4waNUqmYy9g1mw59tijpUongGKpZQ55EcDaB3GcQZoToe1J7dXHht8CJp4BaeVNAWmy5AX/iQAnxvE+iKlgXzItxcogWwdq3NYkLS0tMnxktdY7WnlZaiLGZiLLtBRHsBhw0oMMfeB185pvXi9zvv4VmfLuw80EcOkll8iEiEH3WSZ0UU0n8dyKx1bK3/76N3nh9VpxO1w5/oTjZdasWSZgTNWIYf6TdtgXTUsZXksBRr9gtXvCSYibtK8XTROg4xgnr71oTYQCM1YGOCHHWBn8b8dA3ra1Ubr1b9yYsf6dgUFbHTCkBa0Xw3SS5Y5i+cOPybz5c2TuVdfKxCkT5P77H5CZZxQeNzh8erZYmM6XqMoqBATYWPuirF69Vh5culx27Ngho94xygSM+dinZ/VzEMegEMu0FKeOGXAS1eakLQOMfhFPt/tXdjArA8LQwdQEMPJimd5GLgpjZSCCCEr2G8i0GMg58K/al6WivELG1vSNW5ALLEmBIc0b6ITCUBkUWy24V3jkkUdkzpyLZO6cubJtxxb59tXXyR23/kzOOuszKgkXaadNWBGi83kB8fewPg6z1W3cJKtXrpb7F98r69a/oBJkm0yYMlHOPPMMmTp1qgkYk9dJnA0Iq0GApSZCeSiO6kj0chkjuII3apCEUZaaiNTukSYD1kxoTCcZOnGSo7psJoYIHbi7c7dMGT8lsooI9GHQiGV6izwom4kFrgygXrjl9tvkQ5/8mPzhvrvlokvnysJFC+Vz558vw4fbH9ShLc+damV87UJavfraelm+/FF59u9/k9e3vi5lVeVy6uxTZPqM6XL4xEPz8oCr/MMIDcoyLYUvIQZojupIahCWl1CcM2BoqeEjjQKUh0BmVrtHKgpLTdSmKwPGCVtacBtIQBmzasPmBqkYUSEjxxfmJ4bB9DC9ZdBnb5qWQqp+bt1zcsstP5Rvzvu2DHNi8uPvfk8W/ehnMr7GP2ULdRxjUGCMT1qO5qYGqf3Hc/LHZX+Qp9c/LYjI9e53v0tOOukkmTHjQ1KRiOa7JpbqtF4xm77VydkzSJE2Nve1E8hwUklDN0GqZ5VHVwaMcZXV7tGairScgf1ySuynZpY7ikzTUgxs9fX1csj4sVJRwOEmxkAHYGUQVl/YgGVmmA2gE1ZQv/zFL+UrX71MXvz7i3LSCSfIzboK+NL5F8oRRx8hpeEYvKzlsIp1xXQe/AbuIdY/s06W3nO/LH9ihfxL27lmnDcBzP7kbDnySC9eQNTVIICBznYyQB4Jwv4OEzh0RgFLTUTqYCYgPsE5EcskFB5ZKZMlCZGKwoqBDAO6spj9VJgmWAQYJJv7SEBNTW/K7p7dMm7cwOakYaBBGfxqNn0JenHkwdh/SGdZGUAV9OU5l8oXv/hF2bRpk/z8J7fKeV86z0wAOd0hkNQFmIQK5UNjEbR6udz7x6Xy0iu10tXTJUdMPEI+9clPyeGHTbbyFOpKqbRE8VQ3ANzSFv/KDkyHkpSVAandWTF+zWRAGDpYdMakwqDPXnVUhw7IWM5AAqJYKZAkDliVhCXoLZu3yJDEkMhqgjBoMzyjbln2QopBzN8zQBjGh1b8Ua6af5V87cLL5aMnfUh++6vfyvULrjfpUcCgj/EFHwFup2sinT2z5hlZtvRP0lLfIqMrD5Ajjzpazjrzk1Iz/h3aCe0Z2pFOKWe4x8gTA7kQwGGZ7eCC36M0OBPEAKPdWQ74WDGQaYYeCgZ9WI7qsge3MUOJF3ABhzSSrR0SH17h39utraMdCYNW5icQvgc1DCwlgrRUm85iCf2a8dvM53KlxRCsYrd8c97lcv3NCzXd15VlPhf8PkgL3wulJVNJiev14HiJdDR3yiN/WS7vnXC4TJigK4Mo+eEZLYPbrl1nqA4K2MjJ/A0+gcx72dLEC+Ji/MjjexF1wrUK0F4wGUh3QXpmXkCetM7OlNx771Kpr98kO5uazOnaI4+cJGNrxumAofwRx+YpwiPG9T1abiO1I7xlj/7zgyKhLiq1JNtb9RV+3sE7wp9A+F64PKE0t7VNHPiiD9od9Pavu7W8W9/cLts2b5PNb2zWmrtSVVZlBv4xY8dIWaLMlBsw7a6DuKGP34a97812jXKE29Z/r2l3WEb5ZTAIng/yyNV+ftogp0TeqGuUxH5lUlU1zEsDwr8Jf2ZL8++lWpOSqNB6+oGcTFqEMvRLy+ynQPBM5m/CaRmf4MM4gj5BHA8/XyDSnToOleqoiTzMjdC7gOA6T9lw0HDztiYpLyuToVqm3ryAEB/15g2E7wN+Wqrd1Xrp9/B7CoWW1VUhy2glg3yCzwLbDO2O8Tkoa6LI8yZZg9sE0gU+MXNhqY0DLTg0FgD3g+cyVw7htPA1TC9cHTgwUAS/CdLxCeA6Xxqu5319jixctMh8D+6FPwOEv2emAagXAsnEnZisemyl0YNDfxzou4PnM/POzMuLGTtUBxf90zQg+E2263D9wnl1pFxxdutAO0QH2NB9IB+NM9MQDcuB/xRllOAdSMdzwW/Cvw+usQL4x/oN8vTfVkn95nqZNOVQOX3m6f1UKXgWvwE8fW5MB/0994Oy4Br/DJ0dFSZC9QaC5/EZTgvnH05LpVolHt9jlYR7u1qbZNOLG+X1N94wEwA8zI4bN07Gjj1Q4okKLZlfnpjSVTNFfggGgnZPZNl7QjqA9+cqawCUJ+gXQVq+eoTvBdco4LaGBvPDMJ2RFv490PsbRTgtuN+R3KWT3vDeZ4L7wXPBdeZnZlrQL0Av3MO/fHXKdg1k6xdBHsE18gXNgt+H04J7b3W0y7CyoZHLEHwG1wCutzU2SaLMC26DvApFUM6OpK4Iy3Qw98teKJAH/pl+itkgrf0nIt9kS2tL9qVPkF4oIkU6A3NQIhaZ1ZV9XnPnzpeFCxf43ywAJ/MqITbrqmDpn5dKzcgaY1JYKMKDnQ1An4Sj/9mqHnTSxTI/UUCB4HVzzpwrpNIpl/MvOldmzjzNmF3WTNzjd79YsPjHRKYr9/JBwJi//OVpSXZqTXXVgUlg8vSjIzkVxEno8nJsFvs3igTqJVKhdfO+F4vGejR8s9X+BdCWdKWcEYNC+4XrVFLow2h3VzuGY0tkBYS98kS1VFTZVQyR4BIJe9Ueb9zg0DnSHIIZiAHo2hi+QViO6jBg4l/D9gap0r/9xlT7KYUBSrViZ+MwUBrEjLYF9mXCq7hcaGjYInfduVjOOe88efC+5fLtK6+UJQ8vMROBAUG/aqArlGIksUx06sAPL6ErH3nMBIzp1L8DJxwsx33wGJkxc0akiQDwOg7HCIEwRunA2+hf2YGlO24xjuoIDUZq9yTpnEFMO2k6hgncDljpUOCv3K2xN+MZAIxGZYF1AhneGTFobqzdaITxCYe8y08pDJSOozAurAmMhj2fXGWqr6uXn/70drng/Atk8Z2/lJpJY/XzdrnqW1fJtGnT/Kc8MDZZDTSfYpm+uXmn5yb6kRWyfPlycx0rj5uAMeecfY6cePw0GXNQdLchgI3X0j7QzkwwJtIVHMeFNSueAaRVCk9btHsYLCfFrEGc5aqDhViM5DrE/8wLmC7ZLmUADHZmc8sSrBPI5c5uaU02S0+qR8bU1PS1jS8QlBlewbCDxsZXZmfGoHXXPXfJly/+orGouOa2m2T+NToBHHu8EjS7eAvTUsJYZ1AMfdauXSvLlj5kJoCmN5tk4sSJJmAMJoCBAsbkQ6XD6Tw4rEZZGZBMS1kmmOXSZlbMDDD6BcW5pYJlWurEOCuVwIGjLdKslZP/mResGMg4aQCLJFuwTiBjOfzqxnoZFB+kA01xqwIADcpoVDP0KsPaAgGEMPFCl4h4ATdec6OuBM6Slu1vya23/sysCqKoVGBaShjrTJ0i8Y9Kko1bGnvdRdf9u07GjB0tEydPlFM+NlMOPfww/0E7sNQgEJAo/YJkWspwVAc+btFWZ2gIiz0kmAkT05uQD8tRXTpd4l/ZwZVuymQJNTUD0SYDQoE9lCsh7XXirBPIOBH9yr/rZcy4GrsNGMIADmDoZUyW/3xhvdyy4Hty2mmflmefflo+84Wz5K7F9xh30XnjBWSAML95yKMuwOCzZUuDPPvsGnlg2UMmXkD966/LIbpSm/XxWTL95BlmMhhhTEo5en5jnkcAQwBggjHBoZ0yHfkVi7QO4oyxA3kwNBNQn3L6KokPSeMGiw8jNRVmZUZjwFEd5Tg4KehKY0ObdLV1yYSDx/l3igM6IatBbI7er1m9Wj72sY/JFVdeJyd87ER59NGH5fwLLpCascXVL5H431UTwarnkT8sl1UIGFO3VVIdKZl20jQ58+wzzengTO+mFCkcSDZTpCmYlVLK1MKpGMthWeDIjwFGv+gQe9UygHMmsRLGhEnaM1AhiUGfxN7cM2BMBIBROjCkMiWiLbo0jzVr1khJxWApG2FnloUGZdCoGDVRXV2dLL7rHpkz5+vy1NPPyGWXXSa//d2v5NjDjvKfKB7JJF9N1NnaJZvqNsnyZcvl4eUrpbWrVca+o0YmHzdZTvv07LzmlQwpE4AjNgZwMpbS7qM5kwEcljEGF5wPoEi/2u6MNksQ3N4DZs+AYXDF2kAm0WevOqqjhr0ktAZDTfSaDkiwxn/3+PHWfupxUpMltQ4kkaGzw156+UMPydy582TpPffI6DHVct1118o3Lp8n06dPV4laBzvChMkKiN/VnpL6f9XKypUr5eE/PSjr1j8n5SMrZfpJ0+WMM0+X4xEvoGbgdmBNBjicRrGWUVAEpU4OnaGjZ9AIYS8ZgCM2xuRk1Dv7EBhGMACLPixEYh1m2EuJDfW/FQ+Go7rGLduktLRU9h9ld9AHgFUJgz6Qw/MxGjaEf/GLRXLxFz8ri++7T1cBX5PLr7rKnwBCqxvo6AkFStk669ff4+DaQ0sfkrUvrJOtW7dKPJGQj8+aKdN0AsAqoBAvoXAMxwCsiShqIu09DNNSN1m4L6zs4JwzAJ8xTG8xiDP6BcsRG81RnTFNtse+Rp9IkwFmL4bkCzUIjmDbwjbsJVREW7dtNTrxygOKO2gWBhqUMcMbNVHmkg/qrCefMfECLrzoYonHRsiV3/6eLL7rrtwqFTA9ocESZYUriUCG5qZm+fuzz8jSJctNvABnuCOHT55k3EUjfnDRm/Wk5TDLmggTCqMzO4lm/8oOrPCHzHgGlH5B0e3oJKfCSYxwQpsSVF/BsrZiHTaMtqjUwYXB9FieO4Qllu2hs1c2bpJYT0xOOOHDUkLQR7KWemFrojVPrpY7b7tTzrvgAql9sVZmzpghv7zzLvnClz5n3EXnA2jMkHyjHjpDiaG6Wrf2OVl671L505//JA1btkrNu98hH5/9Ufn4qTNl4uTDrd0tsAYoljURqzxwOM4Akz4M1QwGO0bfSJP0g/HAAaQ1ONZELGur1F49gawE5OjE9w3T0rqNG+XAdxwoUlFCmZwwWdoCXj/r1j0rdy3+vVx04UWycdMmmTptqvzyF3fK+Rd8wZhXRgW8hdIGhjzA6eBn1qyVB+5fKiv/slLeeGOrvGvSO+SjH/6ozDr9dJky5QjjDjyGlQphVGBMcICjy3zOZOlf2ED7lkMKexk44rMGvGISwBrsOAM4+gWDOEQQxg0gECBtEampYLLGmAz2BdNSmDO2dbTJmDFjpAS6UUKDYOC14bOG+jq54IKvyPwbrpEdb7bJbT+9Tb5wnjcBFFVTbS/GYIcldbZhqqmxWZavXC5/+dNf5bVXX5XueLdMnTJVTj39VDl80hFSVa0TgP+sgXEFbD8qOGmER7KHifFLAMW0VPnPbbZXVQJwR8EYfOGOgrFnADDGX9YYzoqBTDPhRXkI7QWPvAxEKgpMlyjH7v/DpqWQDFY++rSUOINl5H4jjW6UIS0gi0LVaK27dsnixXfL/Kvmyy0/+LGcPut0EzDma5d82X/CAtpejJVBOmRaik1FuIV4cvVqefwvj0rz1mYp3z8h7z/q/XL6qWfk926K8hCYHj72KQhiGViCZVoqCXvnaUAhm/H5kHT7RgAsGjrRMdo9RgrDaTaQu+0bLEmSxI0gQCAza7KM3FSMQv+nTUsbNm8WuPE46JAxe/wQETYlo5qWtra2yj33/Ma44J47b75SIyaXXnSpLPrRj+Tjp31cKlSiZpnRMVYGOGeACWDNk2tk6dI/yvoN66UtmZSjjjrKOImbcfJMGTd+3MCmuaRlPktNhEAnNJUTIRvWSgVqGcbAgJUB8rIFy3QS7lUYMH2LwIsOQdUNgD6UyZKx3FH0j2fgJqXNdVQidE3MYhMCz+02DIINYNyH8sAM7PqHe95T8DuEvz1pwe+B4DkcaEFn9GRO7zfha/wWjrJwL+u1Uynz53rBbTyzPi8daW36f7jc4bLhmZc2rJUNdbVy3HHT5N0146WtpVFHhipNwYSg9TOHbTyggwaHk0zd/bTe+7rCCd7pIAJXBd6MDWAE8HH98uJ5/Z1TLWvWrpAf3nKbjKkZI5ddcJknScN0U6VUlBJjClRYyNs4HHM7jdWNZ+aHibQka52y1TcoK3z/9/4+wwd7n7xDabjfquV6vaFB1qxcbcxvu/VvdPloOXraZBlcXiUlMK2DRZD+3tFPR59v1H9VMljbR+miIyRiD4BGKJMDFXSp135t7mCtI940yNAItE/qTApzT1j5JDQRdfWo0tObhmfhZdarU6jNNb8AWdtJEb5vypRs0k+lnfIh3oO8Aa88eK9WL3QfCNLCfG1U66XBakXL5JcPdUe9w3UCf0HixjtNvbQOAR+hPK2a1+iqKpN373uSzVrMar3C2/t+xzOm7j4f4gnjhVfrih5oyqd/YV4J95F8aSgD9lWQd/C9t0wRroO8QXM4g0xKpaa16N1E73MBcB3QOaAx0Oe+liXhVKFQSiv4SfP4FQJYQG+QOKAprrOldSqN8YaSKq9eAaKUAcC1oRj6ppYH9TP0TjZqeUab70DAb5lprrZ9uF2C58ETUekalCF8Db4w79A/82yRapx+k4GLWHVB+MVYqZEQUu0dyheOxJU5zGm3WImZrXEs24TB9L8DsJPvTcPCQ5/HBgcksVQaHbfLVB73UBk8i30EY65ldMs4RanfnaFZr7G0umreFXL9woVmlRFIeHivcWil70S5TRQhvYf6IO+0dsCHljxkAqJ/6pOfNCUKwh9iee0d9tJ36R/yiOt1Sv/3lsvQn3pp2PHAN/wez6H8sMdHqMqAXkHdG+s3yyMrH5Yn1/xDJtWMlRmnzpDDJx0p7qBOrQbCAfqSii9Zu8YBVpcJxQkEtASMGVpGnQL6Z9YX2Xrmb1pabTNDY00z+eifkfp8vWc4bVdzs7zxar00Nu6Q5rZmSXelZcKRk+Sg/Q6Q/UYfIIOQrz5v3gs+0bxN++K9mq/ZyNLv8DKJt6Ns8ViPtKUQEtNr36A+pr30D+U2Vif6Z9L0GXPtl9N86rNIM+2VGNovD1NPfSMGSbQZyoE74TS0I/I1YTlTb+mtEXrfowPyC2igF733QUdHl5JBmpF09XtAbzel/cK0u5YR78Jv3HavbZTHoYLsrZPeR/Qw0+RaL+SB9+D7tm1vmN+MqN6vN+8wTY1BgKGp8qSWz1jX6IBkooihHJoW0KdMBYmAL02ZNQ00CMKRBn0YdM2VhnMz8TjS9L7+wd0B+iradqBrvDfgj3SXvgPhKsHjmrfhD62F4T8gRC/TDvoXpAVtDqS6dJIrgaoRPA9zzCCCGoY/9FWvlYP2RltkS2tq2qb0ickQncC9/uHB8F/wXow3flr4PoA0jBWIdAY+RH1AuzAdg/KBlqBd0BZoT5QDtApon0zt0vzgLrzb9BPTtj5/Be8N3w9+hzTQOKAl2h30SDjh8midQY4CECnSGSoPJrMFJHnHAUH3NEQxmDd/nty84Gb/WzRsUUl3lUq6M2fONBucplMqEZXy1uWBhI1wjOijiBew/JFHpO5f/5TK0WNl5sknytHHHu0/mR+GPjFv0LAB4liDIaIwAyyCXn91uzRua5Cd23bK0IohUrn//jJxIlZOHVIzjhDpLKWdRzuH7ZI4ldSBQ5m+UCYPA+3+lrb7MM3E9mCeGRQwyNllo5OvrlR02LA1vaX107YmiSVGaN3sGozV7slkSiVfuz4KbNu2TQfMchk+wq5/scrjpjx+ZvQLTE62iFQMTzq2h1kqQqK0RDHWRJt0kC7V5SEmAgANgOUVZldb4GTs5s11cvHF58icOXPEGVYmi267Ta65al7kiSAAJAhbmIlA5bR8wMSzduVaWf4nnbhqvXgB7zt6gsyaPVumHX+8VI84QJId+fOIDJUMMQjbAtYytgMv2h3KtWBFaQP0C9vyAKVJzgZpHCt6RldlOarzV1fWcHf5F3YwjuqGGvncCowxDMCKjtIvxFsJ2CJSi6PADCaD7pBh8VBo2EuUf9ub22R8zQT/jodAp2yD1atXy8IFN8rtP71dTjhultz681vlgvPO81MLAwZwRthLo8LQAS8bGuobZPXKVbJs6b2yaesmGX3wQcaEFe6iJ0/se5itmBPIWRFTKZwwtuxr1jKYUBj9ojvB2ZCEiocxORk1DEMAhCqL0O7iDPcv7ABrIumyL1BYxWQFbS8G9voJZAYw2Jk9BksUegK5ftMmowd91zvf6d/x4DnkKkxSQOfH6eCrvvktEyQGITPPO+ccWXDzQjnrnLNkzEFj/CcLR64BvBgEnRkT4ebN9bJ+zQa57/77ZPXTqyUdS8vkyZNl5sdPlenTTjSTQaa7aA+F0TknSNZELIkMm2yslQED0G4zEOiKGaBEz9JxgyH5hvX2NkBRoMe3h/3qAmBZE7EO00XbM+holbKyIv3JhADVRCyWknjcbmadN3eu3Lxwof9tYDz2yApxEo6ceOJ0/46HlrZmKU9UDShNYU/ghedr5aHly+Wtt1pk4oTJcuqsGXKQP/CzdKOuEsiN9Ugibqf3xZ7Bli3bZUdDgzRs32omz5LKEqkZ+04Ze8g7ZHjWgb8/NtXVybgCguHkAuiDTTFbqZXFhy1KZ9aeQUxKxfYMTkNDvfaJMjnggAP8O8UB9IE1GIMP007ces+AsccDtHV0SnmZ/V4IXKaUlw9TwcdyTy7ZIfGEfexdVr/AHoYxZLDMJ1Jrs7ziAQw/I4VKdW++2SIHjc0isWPzbwDdOvzun3PG5+WmH9win/j4TFm0aJFccOH5vROBgUq+lBkeK4OYnf64pb5F/vTYI/L0yiek7vVXzZbIB054v5w28zQ5dNLkyBMBgBjIDLC8ujL4MFDrMKR65ME4jFlRkVDp1166A30YfAhzRlj52AJSOKPdbftEgATMuAkej1Wc9a/sgBjIDGDFzKBzpJVBsrVdEpazKcCSfOfN05XBzf1XBk07d8pDy5bp4P+WEhq28ENUquiQkcMq5bPnnitDMwLeZ7OawJKrftPLsnr1X2Xd2g3y7vfUyOTDpsgxxxzX7/cBwtZENjArJynMMgBjSCrVKhvrNklD/euyq22XOD0xqakZJ6PHjJb9DxpddLwG2sqARZ8O5cMyez5kWcuwJF+WNRHLqgS2+bBKsl058SRfb8Vji6ZtTUofR4YjhKoFQB+cYbAFq1+wrMj2upqIYlo6b75OBgv8bzpobaqXX/zyLvn70yt1sikRHFAOthWC6zPPnC0Xfuki76YPqImGYVmt3Iol5NpnnpOHHlomhx5+qLz/sGPk6KmHaVkH1sNS1URaFu+QUn5AGqirfUU2btwo7al2KdG/d0x4h4zef7QcMHp/6YkNtg7agyhqhcRMzoVUKqW0sV/GstQFrMEO/QKd2bZejQ0NEovHrdVELPqED2/ZgCckcUw50cfLyssLWh1nA00oIY0brPJEKoZtYQPQTEtxPsAHlv3zvjlHnnj6CenQARGDv6PLQXziX5um4/P++5fJ8uVL/F95wClC+P2/av58+eRnPyt/fPxhc37hkksukanTjtZ8Im7IkUwnjcrKHGvNDXSw9evXy9K7HjTuITDQvnfie+WjZ86So99/tHHAl3ZT1hMBoGSkgLUBSHNU55QUrGrMBloMZLeaoibCwS9GeXB4bCD1aSToQMfoFypOGEHSFo7ObowYyDAJpYCkXpa96aiOZUIHnThD7xsObvPL39wpHW96dsiVKg3POOV0ufLbV8r3v/sj+cAxJ8n73vEuTYFVgyu3/eLXRjroau+SVY+tkoULr5JLLr3MqEJ+9bM75I4f3dp7DqEQgOFtpSggl+ktNoRR7ufWPi/LH/qz1NbWSmJEQiYf9l7j02jKlClSER65SVYc8JZBgZaHwvQkE8OE7wbAFixHda7TqPSxJxDDtBR8A4Nrc7LYEjGS9RfcbDD2ZnQgo8RAxqlvCrRfUIQJ0jmDyGoixnLYWCmo9OIddS8e8+Z9XW6++fvS3t4pnzz948q4g1X6d+T7N10rkw4/0jyzZcsWWf3X1XLiSSfqMrxRLr/6Si1Al64eBsn7J0+SY446Ro449AgZN/GdulSzKw9LNwr6pKTHqDAwAeza1SH1G+vktYbXJNWTklK9P27iu2X0yAOlOs+kZZafON5vWaB9bc+AZk0U0YpsILDKA5fg8DRju2fAUqfQ9gxYaqJUUhJx+9mAZU3EojP2eOBtwJY+rD2MSMVAYW07DuCtDOxP2KbTXkP89a/LdZaGvxZXzpw1u3ciAN54Y7POl0NMB6upqZH9R5bpqswTdT999qflnHPOkdFjKq0nAoBlLQMHU7BQQeM+dP/D8uc//0nqXquTdE9aTpp5nHxi9ifk0ImT8k4EBlBbUSQ7QqV8MFYqHJWDpx5kqEHQLxjqC7e0xb+yRRdF0oS/HI4lvUcjW7gpzuEsljUR67wLrK0YPG0cWxIQqalYaiLTARmn7nSwA7Y0toirK4JhZQk5/6Lzzb0Ar7zcIP/890syf/4cufrb35axYydILDFcEm6nbHxxo3mmvLzKuDiwBSYC20bt1FXO+vUb5Jk16+WPSx4SBIyZOP5dcuxxx8qZZ58poyuj+wiChYtxtmYJTLIMgH8YgwKW1QzgBDJjskQeDCFAWkEfewIhBjKjPKCPvdyrIKlBWCd+XeVnRlYUXgaUPvvSZBmtKKRBASsDhs+TIJ5Byp/l96vczzAdTEvvvvs+lfrPkt/de5cceeQRcuX1C+TWn/xIjjlmmlaj08yiHUmvPthcZp0iLQa7du2Suvo6WbniMVn24DJ5qfYFlcg65Phpx8vps8+QKUcdLeNqxvlPFwBMuATbbJjhMajDojErH2yPUlZOLN5RiZWxgcylD0FkxeBLGTg56xRMBhSBgnTugTWu8vpXFJAkMqwMGEyW9ieBYZXDjES+Y/t24yDue9+9QSWjEpkxfaZccsk846E02Fh95dVaTRtiJoAD9/d8Ehm3BARfQIUMLIhwVldXKysfWy0PP/CwrH96vbiOK8eecKzMOvMMmT7tJBPzwMYaCDSOEQYXbLozWt5zu+t/sQBjAAc858b2HYhRJwM3qTSyHzXhSpsBqIkY/YLV7hSneQpaQHyST6F9jT6RcoH5JWvPAButtnAqvcEcnuvjRl/mSlKl2JsXfl/e954J4pa6clCGzfaqlav0f48R3nfoseYTdhMMfy6gz0D9ECuXel0F/OnhR+XZZ9fL1u2vy8iaUXLm7Bk6eZ0iY8eMlRJXpyeXIAVBIiM0WFonKQb2NdNSDL6UlcE+ZlrKUHkCCMhia+QBsNqd5XsnpX2LYRUai9lv1gKgD2VcJdGnnzURLFHCsyc6Tbo1JU6FN9rhvRj4wu8P7gHhtMz76DjpLlfiQz1dYrbfAJm/C+PVV7bLJV+5SIYdMESOmXKCPPXs09LR0myshGbP+oiMH/MeaU22yowPT5eKCm/S+PGtP5Xljz6qk0ePjBn7Xrn1lhtERW9xW3W5V9quDbJHkYhiBK+E/AgJO1y+zLKBPt2trpQMzZKm33ftbJO6hnp5a8ebsrNpp1SMqJCDx9bICJ3QDjroYH0IhFCO0E8zsOzWQc+SYc3+VomWLChMkajftFVqxo0yNMF/yC6gCfYTYMEF9yIBjUwwF/3LpAPK48C+23KFmWodLPEKz4Ea3hF+D4Br3AMyyxDcRxl2t2oeQ3fLYJQ2ym8U2dLcTo+XgYHyCN8HgjR8NjXtwB2prt7PS/QR7iNArvyC+6BzcLg/33MBcqWl27VfDPUCCwF90nL9JnQfwDXKA41K+LnwNTBQfviHISlcr4F+EyBIC+7t3PmW4dmKKs+vUPC78HOgOQbo4Hv4mSAt1e61e+bvAwS/BcJpmffD9Mk1HoZ/A2SmmfKE6BOMJUChp7azmpYGLwsKARMxxnFwY3kR6yzYHcVL/3xJ/vLXv8jK1Wtl2tT3yZpn1sk9d99t0tatfUG+ccVXlSjYNNUXxOMyecJhxhPn5k2b5Km//c0MUvH0bjls0uGy4PvfNwQEYGJYlhiuy0evoqh2QPegccINkQuZ9NnWuE3e1MF/U3297NJ3lOrfgRMOlHHvHC/VVYiwlR1tSV2Bxbrz0icoo99E5hpN71fJAKEi0ZFRr3Bb4jrzM0jLhvpN9f2C2wS/DZD5PRvCprf5yhDcC3fIIA14K9kuwwjuFlimpZ7gZOeoDnXcuROHMTv3meA24ENEzWIGfbJBm7Z7OaHdWaaloE95wpJ5FCyTdFa7Z20mNF64ARGTlgHTaQrYfIF1DQLGfOPybxjz0CX33CWXXqrX4w7ynxA54uhD5cxZnxGnrdHsB0gqJfW1z8q9v/u1PP7UU1LpKGPHVGJ1SuWyK77Rh/AwMQykHyBMDDxXKBMjhvHqlWvk8b88bk4Hd7S1yRHHHS2zz54tx77/2LwTAYCNu4HoExQJn8F1Ji85/mQAhNsy22dwnQ3ZNFaZz+f7fS9CK83wu4PPzHtBG4XTAAQvZQCxiRmASbHtYSjUz+VoHZTMe+hcLMxErH/gIFsg6FMwoduBoNsJ4BLyGsBLQGRov7CdCIA0aXyO1OJOuscwiS1wqGogNG7ZYtxGzJ07V+65Z7HMmHWe3HHH/5jN4ADpVF8KnvvFc+Wy6xbKO0ceqAzoqETSLcl0TCqlW7bqK8eOfaf84Jbv9ZO8oBu1BWyON2/ZISuWr9R/T8gbW1+TUQcfKEcdd5R85OMflYk1hR3agh2HLVyt9z4FS/VQAJhOMhAOom8DdGTbfoHB0mniDC7Q89sOvmZwcpt6hQkbOMIJboM+wRh/YsqH6Zj96XPEt2YA+5WMeiG4DSOfvXoCGQ6wYDOcGc8Aao01K1fJCv0HS5jjp58oE8eNk/H6LxvmzpkjCxct8r95qK2vk3+s/rtMOfIw2bLNG+TLy8rl0COPMHrCbEyJw12JBGIFF7YchtoJEcN2bNmuE8Fm6Up1yeiag2TMmIPk4P0PltIc3k0HAsurK+iJGu0rJ5BZjupYJz/DDgptwIpnwPJaSnPkl3SlTEljfQKZpAZhOWJramqGFtnaayktngFLjUZq90jFQGFtG9RDudlwDIDZ7IabbpIPfeQjctsPfyrnX3Ce3LzgRpk1Y0bOiQBwyjMK4yZlzfLVEi+Jy4RJE2X69OnmH+IPJ7TguYgNEzrMq1GB8kIVtOz3D8jTf3tK6l73TgfPOG2aiRg2XlcBxU4EAGxlKD7OdRlLsZZJUNyVqbSKHW0CSLFwjQM1Bn10ALedCAySHD0Ry1FduXIixbKfZI/PspZxYUVGqBgrngHLkR/anYFIkwE6DoPJYN/t6MDw5KpVsviue2TO1y+UykS5fO+718k9D/7ODKZR4Hb4Fz62qGRVUVUho94xyr8TDYj1OtBJXTRWs0oUG154UZY/BM+nf5F0PC3vnjhejjvpJPnk2WdKRaLSf9oOsH3CysAaLLUMNhL9ayvkWJkVCjfmWYfZAudL0KWtofViuKNwEs3+lR2SLsdRnee1lDBZwlyGAJZaBnAIK0vWngHow+gXcFDIQLSihDYAbbDkzsXy1a/PU6l6rUzUwfSWm26Tiy69SKYePVWZOPrGTnACOcCLtbVmoqmZUPhp3WybL5BEzATw/POybNlDsuzPy2TTy3Vy4NhR8uEPf1ROP/3jcuSUo6RGl/WmJKzBlzP06tKcoxMn8KkHEv+wTlpi0CxkRZgLvPM3HP5hnC3B4AQvoQx3JsbsmMFEpIhgZs+AsDRgHe4DfRgrA8YqF4hUK7idZjB99cRqufrKq+Qbl8+TI44+QoaUFkfU4ARygB07dugwmpDRIwoLDlLu7FYC9C1Da7Mrqx9bJX/685+k9qWXtbE65NCJh8opp35IJ4CjjZO4fhOXDnacYUpBWFqbMHgEBQ8r7CVAYXrCgUWA6aiO0S+klHOYjmVVAvWpKwSBQvsFpd0Zuh0FTtTHLNS4AZjxDCj8Q1LHRRqN4b+boSaaPm1Gv4M1xSAczwC28IP0b8pxk/070QGrEuizMXjCBnnNk0/KQ3+6T7bt2CajRo6Sye8/TD52+mwTL2CgcxaM+BJmgCIs+TBocnTiHKAsHAmRZCXlNtFWYYx+4XRyykLzsy9tmpd3uM8WjHYnCeIq0WufaLdf8bDozLImopXH/8wPkhrEOMBiSApBTEtF/eZNUj3qAKkp0IQTqqDGxgbZsGGD3Lt4ifzlL3/RFcabcviUQ2X2pz8l02dMl4kTJkTyEUSokoHnM8deIgNzMCYDljsKniMtTj7QiTPyYi3PWWoiqC8Y/QtqIoaqkeV7h6HSA+CoLmzAUjw45YEgyigOS20VKRdWJ8SGbYyw8x1zPA6D2+ftW3fIhIjmj1gBwEvo2mfWygO/XyprVj8rjVu2y2HHTpHZsz8us06fJRMnTirCSRynMxtrK/ijsATMOBltxmExhdHV+tcWgEqPIUnBioMBlv07xzcsNhI5OnqjJiKsDFiDHWWzX4E9A7hOsQbDyEPBmizR7gxEygUMz9Bt4SQz42RjENzm36/8W7tjWipHV5vv+YCg48vufVg2PL1BXn3lVSkbWSbTpk6TU2bNlEkTJg6oBsqHKI7qogAxohn6PwQQ2pdWBizdKFZzFB1rkhXPIE0xLXWTdnbvAVgmhixHdQBl7KU5htO1d0irUCxYwjHLUd1eNS2FlQJDAsImL0xLbRGsDHY2NcmBB4/qG/83BMQLqN1QK4+tXCVPPPG0xBIxGTVxjBxzwjFyyoyZMrKmSnYrg9gCDcpg+jZ4UWWY46W7KQwbS3N02VgZMPiHtBrW9uKYqKLNKSsDkmkpy8QQfpsoHlAhiRPaLJ3mxKwGGKalLPUgwFkZ7GXTUsYMhg1SyspAZ/d6lfQbt26TcWP7mpM26wTw7Jr1smrlSnnogYfMZACtzzEfOEpOn326TJ1ylHEXjVKUaIkGU0QXjhrExFcghOEEKJIvYaIEWCsn1oabtzdDmCwpyxSUh5MPS+1gguEzBhgS/7B09NhAplgmsQwZMDARsHbt3/0rO0TqorBOocR6hQUHQQ3ilImsf+JZ6enskeqD9jitW//sWvnzw49Kw6v18sbWrTJmzBjjJA6ng8eO7R82EsfBGYzGioFsTiAzRjtM3rBMsoRDMi3FRMCYDIzJLKFIMC1lTJZod0ZzsUxLcTaAQudkk8RJenHG5MQyLTVhLwmmpSwTZ/RTBn1WrXpMzvjYF/1vxSMS68DhFGtlwJhVY2nklJSRY/aXXc1NugpYLff+7l7ZWPeKDKssl3dMfod8+KMfkWnTp/m/yAFdDjMkRNCGszLQtQGjE5LcLSACGwUqATEGTcZAByDGL6vdKf2CZFrKcuSHfsHgH6xUGGC1OzaQGaalDEErAKNu3/jGlTL5qFEy7+vz/TvFIVJRWIG2sTJgeEOsqtpPWjtbpbGpSVYuXyVvJVvkHRPHy4c/9hE5ZeZMOWLyEQO6iwYSbitJneJfWKNNqUM47MPyTeR/WgMSGSEzRp0AY+JMyosBmpqIMMEBjtut9LFnap41EcuUk2Na6qY5J/xZaqKeQSm55prrZeasGXLVN7/p3y0c/byWfvHiL0tzPQ7leH9GWtVBypFyI42HAe+Y6FjlTkLaXC8Nn/gOhO8nVMqECZ1rPPCI7Ei2yagE8nb6XCPPcgd7C/q+0DUQlGfilInm+462JmmqQ5QoD0gHUCaUGbI27nnf93xCSoUDu+Ae3hMuNxClTuEJMsgbQH6VTnnW3wPZ8sa/rTqpjUpU9qNzIfDayysH6Bq8N/xOIFymIC1zwm9JJq3KE6Y7rpALPgHcTZicE+Ze0DpBWvie96zXvgEfog1RbtwDvdGeqO/IRMA3e9JQLzyPZ7w0lMTjN0f5xOMvaMrL9Rq87sl+3jtBlHBaeW87BSX0aImnPPrjO/gdqXhvkGby1Rt907x2xzOO3x64D4TbCAjaCQineXVt07y9vhiUL3gm+E1wnfmZmQb6BpQPyoi0oNxBPXAP/dbLYU+58TzK0Lct9pRvz7VHF+8dua8BfA/KVAyCdgGCegYI6geE08L3AVwH4xT+gjTwk8fHA9MFdUdpgt+jfsgvGAPxm3z9on9awNNemesa6mT+fG+FcPbZZ5vPqOg3GdT+s1Y6OzpBebzdfKZSXohDAJJ9IDXEgghhLoLHeNeDSwbL7m4/NGHovvmN5peKaV5Yzpbq77s1L1gthK81qaSkRLo7u71rV68dX7Xkl+fe+38vZ57+ae8eihVsQwQaKP1u8ivR/HA4Dyq+IE3zQJlQHjSSo+WBXX64rAB+izzMdbge/v2gPrifTKU8+uA9+j6Tf+g3YZoA2dLC9EnAdFazM8/58vlg/dvtn0HAs+EVVm+a/xsTkjLuGNrtdvzfhOoDDHb1NxlpQRkMTRVbt26VUWNG9a1TlvIA4TIFaSY/hcpjmqWXZuqt70g7aa9t9a8PvZCGvEL38Iky9eHD0H3Dk3pdUurxjUnz275PPn55vHcgzbsuCPqbgCd7y+Pnk61MQVpQtnBaUKaWth0Sc+MyrHJYL+8C4TYCwm2Y2X6Gv7U84rc7ymfeE/pN+J350nrpgwQtb5/8UCek4Vn/9+F7APJAH25v75QE+lappgdtgbIG1/67BrrOpHOJ/hm+QXn0D5/Be8P3ej9hfai/e+stncwTMRkeHx6ZrsF9AGnhdkf5gF7a+Z/o093dWj7XK0NvmyO/zj3lCfoproOxo5feOeqXWXc8b8ozVCeFXUn57g9ukpuvWWCeR7THQhApngEv7GWrOPGh1ifm5s2fJzcvuNn/VjzaUC/EabArjvHbbhuDAGhVSUGpowwFri8eKbdLmVWXsv7AWSyyhb0sBiz+MfUiWFuZdncQX8EuL1a9mhobzXhgG8+gPdUuQ7V/2cLwIQY7S/7Z19p927ZtUjY8LhUJy3gGSuc4gc6u5oPx0BYwrKhveE1uuekW+d73vicVFcXRPNowaMkUAbqdEs4JQJ1RaaCYmnHKU6rLP+hZbZFWGmMJaQsjeTCg/MPIyc0Wh7NIUDY3Sf0CbWU78AII8M/AoGS38tAeyblosOijK28GIE3Huhn9gkNnGDgz8Itf/EoWLFggN910U9ETARCtNKTBrsRNUA6WByeQbeEmob/j5MWA0W0zJstYiTjpPbrOYpFOcZgV/MPIKW3W0vZAu1M2NllCQClMDO3zctP2ZtuAF/SJMFmS6BMjrLoBmJamkgQ6Qx3HAMnb6GETJsudt98pw4cP9+8Uh0hdgmbFodkwTyDbAidRYzFCw0LyJRQJG0EUaSrdLW7MfpKLxYkrA8YcJ8HGjyVgOhns6u0D6OlOSHm5/aloGn1k4KBPexUuYZWiKCsrk7KqPRvHxcKBnp8BUpCc9087wr+yQ6TJgGWypiJZXl/gq1atlOrRB8igQaVy1mc+5d/tj8x4BsXCRQQlxngHyZchabLiB6A80Zo2L3Y2NWtbDJJNDZv9O0UCEuI+JIkbk2JCg0FIsp1THnhgiXzgIx+U/fbbT4488li5ZsH1RdeT1U9NnRhSK0kIEII+AVX6yle+LImSMjn66EPl7rvv8xKKgb9hbg0SfbpNMCJ7ROoRLCHKMYZTuXHuf31R1q19Tnp6OnX2jcuyJUv8lL5wKjm+ZVgOy3DIi0Ej46iOMeARYqtiExEhPYEyx3KVgfIQqkWZcBVJqEEInh4x+Nrs9WOD9TOf+aysWbLaWJ/cfOO35NorrpY1z631nygMrH7qum0ct8ja6Ixs4ODSFmd97AypqjpAx5YeWbHiUbn88nl+SuGwCW5zz+J7zGRkoBNu0E8RWx2CVzFwtL0YiNRULEd1SahlcmxMdXWm5WCVjuBCAjjrE2fKM+uz+9xw37LXhwOwdGBskqY7OW4SQB9bCxeDdLcxmbXBxZdcKFd/4xvmOpmypLcuhyljC0kgA6hSdJHo2e3IfffdJ93V3Sa40vQZM839lStWm89CEbc1i/MBR3VGZWkLlXwpQhJhM/uoE46Sz376TNnV2iqVlaPFSRQ/wQwk1ObDU88+JafM+KT3Rftp0C8SieIFXBf+eQiIxj06wzMGO6hBcnXCjrZdcsTRx/rfRI47bqpKTtmXh5kxkIuFCSBOmAxiJRy7G/glYviRR2ASWx/nd/74Z/KZT/tnOWxBWg7TTg2TdLVmsLOYVEqHlsqpp56KZZj5vnrVSvN5zjlnmc9CwbJOQb+gmFWQVgaM3oWDWEcc+375/OfPkdLSUrngC+f6KYUjLYNl3dp1Urexzr/jYWfzTnlh3Qv+t+xYsWKlHD9tqrkOjz3ZJt9//vOf5j1dyq/1dfXSuKXRON5ccPNCue3H/197Vx9b5VXGn13e3t5+QZ1WUEJMXVpC55BUPhRDYohhSMhClnQZq4EYzZoMkHV2w67TdgqRGdwy3XQqZCCyiSSUjEyi2Rb2UZj9g8jGulizElzCQoEW6Me9bS+3Pr9z37d9e3tvvfeeX8zU99c0933Pe+95n/Oc5zzn6znP86wMYGVDs3j5+CvS1tZm0hDjJW/gnMG/w0B0zL2yQzSq/2Pp8+rr7RvfvmW7ezf93o/vbU+fnitATwZyckI0eoOUT2b+5ALQMz6mmVkCdQAR6e7pdlPyg6GHAKYcMuprYOCGycsWPV09473K66qqqvEzZ864qbnjP9FOc8HHrd4hzwD4XRqZlzd94M2WLfeNRyKRKXk0NDSM33P3Pe5dGkT7TXvy2iZ+62ezXx1fvHjR3OM9APJetWqVSfP/79+7d8p9Jp2ZDbLqt+GojjHdM9OrDI7qHB3t9/dP+nW/0nfFpKWDPwayDVgOywDGCGgm/uSCkFOiMwP7gBfmpKTCxI61BGNmwIr1ioh7DGsZzJYj9sYp8okF5XL/A/XS2tpq4m3nC7RTBtAuKC2MNCNktAkAJ34Hrl+XykWV8q2GOnm786z7JEdoPs88c0i+smKV/KjtJyaps/OUHDlyWHbubjX36fCdB7fLHXfcrhXlCo3yx9Mbg4OTMRsQjfHOb9wpO1pazHuAkbERuXDhguzdv19iY8PS8njyPT97+ik5/ebrZi9k1xO75PiJ4yY9H2SlwliO6mZCUUlEOk6/MTHNaW9vl0/N+6y5ToU/BrINjNcPRng/zYcBeIRhWAGZtUhYSlkiwbJuInQmAG2ZCCBYy4AeW9fuhw8fkZW1X5VtDY9IfX29m5ofWF5L4eKb0S6gNBmw3f8Cqmtq5OjRF8UpSnZzf3//HzL/M3PNdc5weXPg0D559te/Mge+7vvmJvn5k89JVVWNeZYK6LVDB/4oa9asd1OmwtOvv923T6o/Xy3r162V3Tt3JhMVGJBtrN8o3968WQqdItmxvdGkr197lyxZvsxcf7/pUenp6THX+SArzYPKYMwM0CNmUnbYOP3xrp/KF5d9Qaqrq+VPf3lJmh7a5j6dCtaeAcBQmqzZBTonxvqooYdhLROy1HQeSEqBx2fMwAj8UXpsZgYYpd57b9Jia+uDW6Wmusb8Y+03HzCUpkH8shbOvl2wZgaMTu71V1+VYy+dkC8tWSaLa2tl7do1qrizi52eCu8E8oL5C6T54WZpbm6W2xctlPrNmfd69v9OR/Q6crh7Q9JIwMDXLjz92vbDR6U0Mk+u9g8lE1zgwFwkPF3YwsWTczjb1Ymsfg5CGTODwcGPlODM1jIbN9ZJd9cH0t3dLSdfe8t0EOlAO2cAkyyCUgB/GMtELNNSyilmxY3eYTP9rEwTGCgnEExdAVKxkqalJNjMDMrmzDH87erukq5z55Kf+r9l2xb3G7mBMmADnAoJM3wFqCwz9IaTsDedhN+nP584IV1d5+SdM2eksTE5ss4HIZ+DxtMdHeYTG8MwFc4E+EUCapf6lgF97cLoIsXBgy/K4Zf3yW+e+6XE+ieFazTVFUvC59OIdJI5KxVGi4FcWqGFJ5xAZp0A/JgFt9G+3wiINTQPRrkSrBPIJNNSRh4GoIfBH8zlCKJ4Ga7YL+lo3BI0/sigdgWEXQOdGVA6KMfOzYKHS8pjzMZs4cUzOPnaSTl56g3p+GuHrFixTHbvfNqkp8Oxo8dk06b7pzruS2Naunr1alm3ep3ctWGDNP6gyaQB4ZSzPomQr+Mh7alkJz6kHn4m09JcQBg8GySDeBDWRlnTYXQGDLPHONxHM9Z8SZ0BiT+sERANpHaB/WwsA1hD+cwAy+Qa/GF0UIwBJBNYjoOJZ11dnbS3H5GVy1fK888fkKd+8YS83fmW+61JoAM6++5Z2b27zU1Jwu+0M7XT/MPvX5AXDh6QXbuSv0k14vAvt9Oaqfs5I1gxP7G+ynHExhF6OOSKi33UIlYMZAPCzADLa4xyhYjuMRj8SaiSYoAVAxmKjhEbvCjG6eTg7Z4BFn8ARmfAmvHAM2xBISEzbaM1i2uk9su1svprXzdJlZWV0vjwDvnu1gfMvR9vdrwii6oWTXNRjv1BTx2Wlk5dusQZlObmFnnsscflVOcpmTVranv2lyMs9paDwLR4BvDNDyde8N0SUYUyKuOSGBqUeKFOiUMR/Z+lvdiI6uPJzU64FnbcaYxRRPoc8KcDuEePhqPuodAtygjNG1Pt0E2jvELuSCKOZQ6lA9c4ih7GNEgrErOKm5rY+kiL7NyzxygH9K74S83PCLP+Dsx2nPTPRkcHJXJLiSQK9Dk6PIzKQyiT0oyRWqZrnPTEXoOOVOF4LzqkVJYUm7xh0on11nioTH+SHOWbIBbowDCydWlCfuDFFLoTyuexYq1pvVOaMVOYyEN/m+RDgSrpAc1fp5WhcX1+c1rZR4fGBI4e/TRM5/dk3tN+r3kWhAvlnx+cl/m3VZm6UFL1udZLGnomyuSgDpP0YCrtyUpiROu1CLKj74UlhvsbHOs3jgv1HtLkPUsGvi803zF5gFaJarlUngqTcQgwWsQ7w/pOz/IFdYj8cBAsonmPgi7NOaL0xDTd0ef4HerdCbunNrUeYUSAPMKJYUkYVxVT68jj+WhI61hzhBdNtJH4kMpoiX4fcqMyAVn0eIkDYAgqj/ebka2+J1UO43o9rvJ87XKvviMsFZ+crWXXrML6G72YlBvIKwKhlMko3qXX/megP4F2G40pn2eb96LsHt2QldQ6n+mZxx+zv+fyYoJ25aH5Xobfg1/gvxOao/XVP1HvKDOeQyadhBtu1s0DPE995vER30GZlWNT6n0merQEyoMCGVY5QnCduFaho3rs0uWrUhwulbI5YX0HgLpRmdI6MBaTKXxI12Zgvnvp6hUZ7otJaXmpVFSUazZJ3TGgeuDihV5ZuHihDhBBE+q80MSriOl7Fsz/nEmHXgurXgN9kKeE6lUlXrrf6ZaaJTWmfoGr1welr/eafPrWcrk2PCzFxY7KyK2GVjjYfK/zXZl32wItj9YB/lRuzv3tPVm6fKn5fa7IKrjNcCwqxZHpI1ZUCgpmBBjy6t7jE/Cu8QlgFAWPo7bH5pseapI9T+5x7/JHDK6MnWJrelhBPMDHuAqibaAcBANBPCjbcp1//7yxybYFiz+Z5DBXDMa0WavA5jtb8eSdVa6PPvxQ+4KIzJ1b4abkB1aQJdi8o1z58scD+IMOzGv/+QKeCCKEs0XYl4kUF0tZWf4BZaDPRkc59KC+whj4WvJneHhEOwp7NzZZkZFpnd8rhCc03j0+/dd+MKwUnNnTTazyAc2uXysUCsIWJg93VGADHJdnlMsh+QNk8SdEimdQauLQ5o8JJanloiwTlWGEas8glp/9ZDwDAgiKDvBWGmxh9mUK7PQPysOiB7MZb+Bsg1CIY12ZVVVhmsRozADjMAvLUR3LqgT52I6igAgCtWsDsgUjZgQQIwQCMUhMWk3YIJHIbLqXLdD4MAjAUoItsDTDOIEcjRKER2GW1gjACW1Wu2AoO5SLoX+wCZsgRDpj8ZnVLiiBiBTZkUIYtQA47IO1VFtwGAh6sGJHaIgqZAxhjcVVs2Ct1xIMHgMMNxQGJPlhhKqE7MBaxuz/WAL7ZoyZAeSQAZbVTcQpSO452ALKl9AZYN2eMdgyYMy8SXw2+50U/pDocT9nhNmYI1QGNmAwNbIFRYErENzGnEa1BNOaCJud1lAec8rlXhDAEHpMzxnKt9zhWF+g3hkzg3jRNffKDsYIggAsomGz3RqkQQA2eRkwMwNCVqEQZxkNhi8MvcGq96w2kAMECBAgwP82SAsuAQIECBDgvxlBZxAgQIAAAYLOIECAAAECBJ1BgAABAgRQBJ1BgAABAvzfQ+RfTltNtDug6wgAAAAASUVORK5CYII="></p>
<p><span style="background-color: #ffffff;">lines parallel to the <em>x′</em> axis through X and Y intersecting the worldline<em> ct′</em> at points shown ✔<br></span></p>
<p><span style="background-color: #ffffff;">so Y/lamp at the end of the bridge turned on first ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow lines drawn without a ruler <br>Do not allow MP2 without supporting argument or correct diagram.</span></em></p>
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><img src="data:image/png;base64,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"></p>
<p><span style="background-color: #ffffff;">light worldlines at 45° from X <em><strong>AND</strong> </em>Y intersecting the worldline <em>ct′</em> ✔<br></span></p>
<p><span style="background-color: #ffffff;">so light from lamp X is observed first ✔</span></p>
<p><em><span style="background-color: #ffffff;">NOTE: Allow lines drawn without a ruler.<br>Do not allow MP2 without supporting argument or correct diagram.</span></em></p>
<div class="question_part_label">c(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
<p><em><strong>ALTERNATIVE 1</strong></em></p>
<p><em><strong><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>t</mi><mo>'</mo><mo>=</mo><mn>1</mn><mo>.</mo><mn>09</mn><mo>×</mo><mfenced><mrow><mn>0</mn><mo>-</mo><mfrac><mrow><mn>0</mn><mo>.</mo><mn>4</mn><mo>×</mo><mn>2</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>3</mn></msup></mrow><mrow><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac></mrow></mfenced></math> </strong></em><strong><span style="background-color: #ffffff;">✔</span></strong></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">= «–»2.9 × 10<sup>–6 </sup>«s» ✔</span></span></p>
<p> </p>
<p><em><strong><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">A</span></span></strong></em><em><strong><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">LTERNATIVE 2</span></span></strong></em></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">equating spacetime intervals between X and Y<br></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;">relies on realization that <math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>x</mi><mo>'</mo><mo>=</mo><mi>γ</mi><mfenced><mrow><mo>∆</mo><mi>x</mi><mo>-</mo><mn>0</mn></mrow></mfenced></math> <em> eg: </em></span></span></p>
<p><span style="background-color: #ffffff;"><span style="background-color: #ffffff;"><em><math xmlns="http://www.w3.org/1998/Math/MathML"><msup><mfenced><mrow><mi>c</mi><mo>∆</mo><mi>t</mi><mo>'</mo></mrow></mfenced><mn>2</mn></msup><mo>-</mo><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>09</mn><mo>×</mo><mn>2000</mn></mrow></mfenced><mn>2</mn></msup><mo>=</mo><msup><mn>0</mn><mn>2</mn></msup><mo>-</mo><msup><mn>2000</mn><mn>2</mn></msup></math><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: bold;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">✔</span></em></span></span></p>
<p><math xmlns="http://www.w3.org/1998/Math/MathML"><mo>∆</mo><mi>t</mi><mo>'</mo><mo>=</mo><mo>«</mo><mo>±</mo><mo>»</mo><mfrac><msqrt><msup><mfenced><mrow><mn>1</mn><mo>.</mo><mn>09</mn><mo>×</mo><mn>2000</mn></mrow></mfenced><mn>2</mn></msup><mo>-</mo><msup><mn>2000</mn><mn>2</mn></msup></msqrt><mrow><mn>3</mn><mo>.</mo><mn>0</mn><mo>×</mo><msup><mn>10</mn><mn>8</mn></msup></mrow></mfrac><mo>=</mo><mo>«</mo><mo>±</mo><mo>»</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> <span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;">«s» ✔</span></p>
<p> </p>
<p><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"><span style="background-color: #ffffff;"><em><strong>ALTERNATIVE 3</strong></em><br></span></span></p>
<p>use of diagram from answer to 4(c)(ii) (1 small square = 200 m)</p>
<p>counts 4.5 to 5 small squares (allow 900 – 1000 m) between events for A seen on B’s <em>ct</em> axis ✔</p>
<p><span style="display: inline !important;float: none;background-color: #ffffff;color: #000000;font-family: Verdana,Arial,Helvetica,sans-serif;font-size: 14px;font-style: normal;font-variant: normal;font-weight: 400;letter-spacing: normal;text-align: left;text-decoration: none;text-indent: 0px;white-space: normal;"><span style="background-color: #ffffff;"><math xmlns="http://www.w3.org/1998/Math/MathML"><mfrac><mn>950</mn><mrow><mi>γ</mi><mi>c</mi></mrow></mfrac><mo>=</mo><mn>2</mn><mo>.</mo><mn>9</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup><mo>±</mo><mn>0</mn><mo>.</mo><mn>2</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>-</mo><mn>6</mn></mrow></msup></math> «s» ✔</span></span></p>
<div class="question_part_label">c(iv).</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">a(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(i).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(ii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(iii).</div>
</div>
<div class="question" style="padding-left: 20px;">
[N/A]
<div class="question_part_label">c(iv).</div>
</div>
<br><hr><br><div class="specification">
<p><span style="background-color: #ffffff;">Two protons are moving to the right with the same speed <em>v</em> with respect to an observer at rest in the laboratory frame.</span></p>
<p><span style="background-color: #ffffff;"><img src="data:image/png;base64,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"></span></p>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Outline why there is an attractive magnetic force on each proton in the laboratory frame. </span></p>
<div class="marks">[1]</div>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain why there is no magnetic force on each proton in its own rest frame.</span></p>
<div class="marks">[1]</div>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px; padding-right: 20px;">
<p><span style="background-color:#ffffff;">Explain why there must be a resultant repulsive force on the protons in all reference frames.</span></p>
<div class="marks">[2]</div>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">moving charges give rise to magnetic fields<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">magnetic attraction between parallel currents ✔</span></p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">protons at rest produce no magnetic field<br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;"><em><strong>OR</strong></em><br></span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">mention of<em> F = Bev</em> where <em>B</em> and/or<em> v</em> =0 ✔</span></p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p style="text-align:left;"><span style="background-color:#ffffff;">there is a repulsive electric/electrostatic force «in both frames» ✔</span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">the attractive magnetic force «in the lab frame» is smaller than the repulsive electric force ✔</span></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">in all frames the net force is repulsive as all must agree that protons move apart </span></p>
<p style="text-align:left;"><em><span style="background-color:#ffffff;"><strong>OR</strong> </span></em></p>
<p style="text-align:left;"><span style="background-color:#ffffff;">mention of the first postulate of relativity ✔</span></p>
<div class="question_part_label">c.</div>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question" style="padding-left: 20px;">
<p>Candidates usually realised that the magnetic field was due to the motion of the protons and that in the proton rest frame there could be no magnetic field. The answers were too often poorly worded and the candidates appeared to reword the question without providing a clear explanation.</p>
<div class="question_part_label">a.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>Candidates usually realised that the magnetic field was due to the motion of the protons and that in the proton rest frame there could be no magnetic field. The answers were too often poorly worded and the candidates appeared to reword the question without providing a clear explanation.</p>
<div class="question_part_label">b.</div>
</div>
<div class="question" style="padding-left: 20px;">
<p>A few candidates mentioned that there was an electrostatic repulsive force between the protons in both frames. However very few realised that there <strong>had</strong> to be an overall repulsive force in both frames because of the relativity postulate.</p>
<div class="question_part_label">c.</div>
</div>
<br><hr><br><div class="question">
<p>Outline the conclusion from Maxwell’s work on electromagnetism that led to one of the postulates of special relativity.</p>
</div>
<h2 style="margin-top: 1em">Markscheme</h2>
<div class="question">
<p>light is an EM wave</p>
<p>speed of light is independent of the source/observer</p>
</div>
<h2 style="margin-top: 1em">Examiners report</h2>
<div class="question">
[N/A]
</div>
<br><hr><br>