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 $0.93~N$
