Answer
The average force of air resistance has a magnitude of 1.7 N.
Work Step by Step
$v_0 = (120~km/h)(\frac{1000~m}{1~km})(\frac{1~h}{3600~s}) = 33.3~m/s$
We can use work and energy to solve this question. Note that if the ball slows by 10%, the final velocity $v$ is $0.9\times 33.3~m/s$ which is 30.0 m/s. Let $W_R$ be the work done by air resistance on the ball. Therefore,
$KE = KE_0 + W_R$
$\frac{1}{2}mv^2 = \frac{1}{2}mv_0^2 - F\cdot d$
$F = \frac{\frac{1}{2}m(v_0^2-v^2)}{d}$
$F = \frac{\frac{1}{2}(0.25~kg)((33.3~m/s)^2-(30.0~m/s)^2)}{15~m}$
$F = 1.7~N$
The average force of air resistance has a magnitude of 1.7 N.