## College Physics (4th Edition)

Published by McGraw-Hill Education

# Chapter 7 - Problems - Page 263: 24

#### Answer

The magnitude of the average force of air resistance is $0.93~N$

#### Work Step by Step

(a) We can use conservation of momentum to find the speed of the ball just after the collision: $m_2~v_2 = m_1~v_1$ $v_2 = \frac{m_1~v_1}{m_2}$ $v_2 = \frac{(0.030~kg)(200~m/s)}{0.15~kg+0.030~kg}$ $v_2 = 33.3~m/s$ The speed of the bullet and ball just after the collision was $33.3~m/s$ (b) Let $W$ be the work that air resistance does on the ball and bullet. We can use energy and work to find the average force of air resistance: $KE+W = U_g$ $F~d = U_g-KE$ $F = \frac{mgh-\frac{1}{2}mv^2}{d}$ $F = \frac{(0.18~kg)(9.80~m/s^2)(37~m)-\frac{1}{2}(0.18~kg)(33.3~m/s)^2}{37~m}$ $F = -0.93~N$ The force of air resistance is negative because air resistance does negative work on the ball and bullet. The magnitude of the average force of air resistance is $0.93~N$

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