Physics for Scientists and Engineers: A Strategic Approach with Modern Physics (3rd Edition)

Published by Pearson
ISBN 10: 0321740904
ISBN 13: 978-0-32174-090-8

Chapter 4 - Kinematics in Two Dimensions - Exercises and Problems: 47

Answer

The runner will reach home plate 0.27 seconds before the ball reaches home plate.

Work Step by Step

We can find the speed at which the ball was thrown: $x = \frac{v_0^2~sin(2\theta)}{g}$ $v_0 = \sqrt{\frac{gx}{sin(2\theta)}}$ $v_0 = \sqrt{\frac{(9.80~m/s^2)(65~m)}{sin(2\times 30^{\circ})}}$ $v_0 = 27.1~m/s$ We can find the time it takes the ball to reach home plate; $t = \frac{x}{v_x} = \frac{65~m}{(27.1~m/s)~cos(30^{\circ})}$ $t = 2.77~s$ We can find the time it takes the runner to reach home plate; $t = \frac{d}{v} = \frac{20~m}{8.0~m/s}$ $t = 2.5~s$ The runner will reach home plate 0.27 seconds before the ball reaches home plate.
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