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02_InstSolManual_PDF_Part13 - Motion along a Straight Line...

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(b) and let gives (c) At the maximum height, Let gives gives Reflect: The acceleration is downward, throughout the motion. The velocity initially is upward, decreases to zero because of the downward acceleration and then is downward and increasing in magnitude because of the downward acceleration. 2.55. Set Up: Take to be upward and Solve: (a) with at the maximum height gives so (b) Consider the time to the maximum height on the earth. The total travel time is twice this. First solve for with and gives Then gives The total time is Then, on the moon with and gives The total time is 18.4 s. It takes 15.3 s longer on the moon. Reflect: The maximum height is proportional to so the height on the moon is greater. Since the acceleration is the rate of change of the speed, the wrench loses speed at a slower rate on the moon and it takes more time for its speed to reach at the maximum height. In fact, which agrees with our calcu- lated times. But to find the difference in the times we had to solve for the actual times, not just their ratios.
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