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PHY 201
Your 'cq_1_08.2' report has been received. Scroll down through the document to see any comments I might have inserted, and my final comment at the end.
** CQ_1_08.2_labelMessages **
A ball is tossed upward at 15 meters / second from a height of 12 meters above the ground. Assume a uniform downward acceleration of 10 m/s^2 (an approximation within 2% of the 9.8 m/s^2 acceleration of gravity).
• How high does it rise and how long does it take to get to its highest point?
answer/question/discussion: ->->->->->->->->->->->-> :
At max h, v_f = 0 m/s.
Using the second equation solved for ‘dt
‘dt = (v_f-v_0)/a = (0 - -15 m/s)/(10 m/s^2) = 15 m/s / 10 m/s^2 = 1.5 s
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Good, though it was unnecessary to use the equation to answer this question.
It should be clear from the meanings of the quantities that to lose 15 meters/second at 10 meters / second^2 requires 1.5 second. You would lose 10 m/s during the first second, another 10 m/s during the next, and would come to rest halfway through that second.
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Now using the first equation
‘ds = (v_0+v_f)/2 * ‘dt = (15 m/s + 0)/2 * 1.5 s = 15/2 m/s * 3/2 s = 45/4 m = 11.25 m. So this is in addition to initial height so total height is 12m + 11.25 m = 33.25 m
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If you average the 15 m/s initial velocity and the 0 m/s final velocity for this interval you get 7.5 m/s, which multiplied by the 1.5 second time interval gives you the 11.25 m of displacement (which will of course be added to the 12 m initial height, as you did).
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• How fast is it then going when it hits the ground, and how long after the initial toss does it first strike the ground?
answer/question/discussion: ->->->->->->->->->->->-> :
Find v_f when ‘ds=-12m
V_f^2 = v_0^2 + 2*a*’ds = (15 m/s)^2 + 2*(-10 m/s^2)*(-12m) = 225(m^2/s^2) + 240 (m^2/s^2) = 465 m^2/s^2
V_f = ‘sqrt(465 m^2/s^2) = +/- 21.56 m/s Since v_0 is positive, this will be the negative result. -21.56 m/s
Find ‘dt when ‘ds=-12m
‘dt=(v_f-v_0)/a = (-21.56m/s - 15m/s)/(-10 m/s^2) = (-36.56 m/s)/(-10 m/s^2) = 3.656 s = 3.7 s
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Very good, but check my notes about more intuitive ways to reason out the first two questions.
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