Question asks students to find the time taken for an object thrown vertically upward from a platform to reach the ground. Set up randomly chooses environment to be on Earth, Mars or the Moon and uses appropriate acceleration due to gravity. The initial velocity of the body and height of the platform above the ground are randomly selected. In this version students are expected to write up their working and submit it seperately to the Numbas question. Students are expcted to recognise that only the positive solution has physical significance.
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\nUsing the quadratic formula we have \\begin{align} t&=\\frac{-b\\pm\\sqrt{b^2-4ac}}{2a}\\\\&=\\frac{-\\var{b}\\pm\\sqrt{\\simplify[!collectNumbers]{{b}^2-4*{-a}*{c}}}}{\\var{-2*a}}\\\\&=\\frac{-\\var{b}+\\sqrt{\\simplify{{b}^2-4*{-a}*{c}}}}{\\var{-2*a}}\\text{ or }\\frac{-\\var{b}-\\sqrt{\\simplify{{b}^2-4*{-a}*{c}}}}{\\var{-2*a}}\\\\&=\\var{ans2}\\text{ or }\\var{ans}\\end{align}
\nSince we can assume that \\(t\\ge 0\\) we can ignore the negative answer and conclude that the ball will reach the ground after approximately \\(\\var{precround({ans},2)}\\) seconds.
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", "templateType": "anything", "can_override": false}, "ans2": {"name": "ans2", "group": "Ungrouped variables", "definition": "(-b+sqrt(b^2+4*a*c))/(-2*a)", "description": "negative root of quadratic equation
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\nFind the time taken for the ball to reach the ground. Write your final answer in the box below and show full working on your handwritten notes.
\n\\(t=\\)[[0]]sec (round answer to 2 decimal places)
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