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  <question type="stack">
    <name>
      <text>5.1.1.8</text>
    </name>
    <questiontext format="html">
      <text><![CDATA[<h4 class="HELM_exercise"> Exercise </h4>
<p>Imagine that a satellite is falling towards Earth at \({@a@} \, \textrm{ms}^{-1} \) when a booster rocket is fired for \({@b@} \, \textrm{s} \) accelerating away from the Earth at \({@c@} \, \textrm{ms}^{-2}.\)</p>
<ol class="HELM_parts">
    <p></p>
    <li>
        <p>Write down a corresponding linear function that would describe its velocity during the booster stage, assuming away from earth is positive.</p>
        <p>\(v =\) [[input:ans1]][[feedback:prt1]][[validation:ans1]] with the following constraint [[input:ans2]][[feedback:prt2]][[validation:ans2]]</p>
    </li>

    <li>If you were to sketch the function where \(v =\) velocity towards the Earth and \(t\) is the number of seconds, the gradient would be [[input:ans3]] [[feedback:prt3]] [[validation:ans3]] and the \(v\) intercept would be [[input:ans4]] [[feedback:prt4]]
        [[validation:ans4]] </li>

    <li>If you were to sketch the function where \(v =\) velocity towards the Earth and \(t\) is the number of seconds, the gradient would be [[input:ans5]] [[feedback:prt5]] [[validation:ans5]] and the \(v\) intercept would be [[input:ans6]][[feedback:prt6]]
        [[validation:ans6]]
    </li>

    <li>
        <p>At what time would the velocity of the satelite be zero?</p>
        <p>\(t = \) [[input:ans7]] \( \textrm{s}\) [[feedback:prt7]] [[validation:ans7]]</p>
    </li>

  <li><p>What is the value of the speed at the end of the booster stage?</p>
    <p>\( v = \) [[input:ans8]] \(\textrm{ms}^{-1}\) [[feedback:prt8]][[validation:ans8]]</p><p></p></li>

</ol>]]></text>
    </questiontext>
    <generalfeedback format="html">
      <text><![CDATA[<ol class="HELM_parts">
    <li><p>As the acceleration is constant we can use kinematic equations \(v = u + at\), from the question we can input \(u\) and \(a\) into the equation. As the conditions state away from the earth is positive we know acceleration is positive and initial velocity is negative.</p>
      <p>Therefore \(v = {@ta1@}\) with constrain {@ta2@}.</p></li>

    <li>This question the main difference between part a and b is the conditions that the direction of the velocity is to be taken as positive towards the earth, therefore the gradient (acceleration) is now -{@c@} and the v intercept is now {@a@}. </li>

    <li>The values from part a for gradient and intercept should be copied into these boxes.</li>

  <li><p>As we know \(v = u + at\), we can substitute the numbers in so we get the following:</p>
    <p> \(0 = -{@a@} + {@c@} \cdot t\)</p>
    <p> So \(t = {@ta7@} \, \textrm{s}\)</p>
    </li>

  <li><p>As we know \(v = u + at\), we can substitute the numbers in so we get the following:</p>
    <p> \(v = -{@a@} + {@c@} \cdot {@b@} = {@ta8@} \, \textrm{ms}^{-1}\)</p>
    </li>
</ol>]]></text>
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      <text><![CDATA[a: rand([6,7,8,9,10,11]);
b: rand([4,5,6,7]);
c: rand([11,12,13,14,15,16]);
ta1: c.t-a;
ta2: 0<=t and t<=b
ta3: -1*c;
ta4: a
ta5: c;
ta6: -1*a
ta7: a/c
ta8: c.b-a

]]></text>
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      <text/>
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    <questionnote format="moodle_auto_format">
      <text>\( u = {@a@} \, \textrm{ms}^{-1} , \quad {@b@} \, \textrm{s}, \quad a= {@c@} \, \textrm{ms}^{-2} \)</text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:green;"><i class="fa fa-check"></i></span> Correct answer, well done.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:orange;"><i class="fa fa-adjust"></i></span> Your answer is partially correct.]]></text>
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      <text><![CDATA[<span style="font-size: 1.5em; color:red;"><i class="fa fa-times"></i></span> Incorrect answer.]]></text>
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        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt3-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt4</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt4-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt5</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt5-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt6</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt6-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt7</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt7-1-F</expectedanswernote>
      </expected>
      <expected>
        <name>prt8</name>
        <expectedscore>0.0000000</expectedscore>
        <expectedpenalty>0.1000000</expectedpenalty>
        <expectedanswernote>prt8-1-F</expectedanswernote>
      </expected>
    </qtest>
  </question>
</quiz>
