College Physics (4th Edition)

Published by McGraw-Hill Education
ISBN 10: 0073512141
ISBN 13: 978-0-07351-214-3

Chapter 4 - Conceptual Questions - Page 145: 3


Yes, the demonstration would still work.

Work Step by Step

Yes, the demonstration would still work. Let down be the positive direction. For a moment, let's suppose that the vertical acceleration is zero. Let the arrow's initial vertical velocity be $v_{0y}$ and let the arrow be a height $h_1$ above the monkey initially. Let's aim the arrow directly at the monkey and let $t$ be the time it takes for the arrow to hit the monkey. We can consider the vertical displacement of the arrow: $\Delta y = v_{0y}~t = h_1$ With no vertical acceleration, the arrow would hit the monkey. Now let's consider the same situation with a vertical acceleration of $g$. We can consider the motion of the monkey: $\Delta y = \frac{1}{2}gt^2 = h_2$ We can consider the motion of the arrow: $\Delta y = v_{0y}~t+\frac{1}{2}gt^2 = h_1+h_2$ In this case, the arrow would also hit the monkey.
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