University Physics with Modern Physics (14th Edition)

Published by Pearson
ISBN 10: 0321973615
ISBN 13: 978-0-32197-361-0

Chapter 5 - Applying Newton's Laws - Problems - Discussion Questions - Page 159: Q5.23

Answer

The time required to reach maximum height is less than the time required for the ball to fall back down to its starting point.

Work Step by Step

$\sum F = ma$ $a = \frac{\sum F}{m}$ As the ball is going up, the force of gravity $mg$ and the force of air resistance $F_a$ are both directed toward the ground. $a = \frac{\sum F}{m} = \frac{mg+F_a}{m}$ As the ball is going down, the force of gravity $mg$ is directed down but the force of air resistance $F_a$ is directed up. $a = \frac{\sum F}{m} = \frac{mg-F_a}{m}$ The magnitude of acceleration is greater when the ball is moving upward. Therefore the ball will come to rest at maximum height in a shorter time than the ball takes to return to its starting point.
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