Answer
After the man catches the ball, the man is moving with a speed of $6.65~cm/s$
Work Step by Step
By conservation of momentum, the final momentum of the man and ball is equal to the initial momentum of the ball. We can find the final speed $v_f$ of the man and ball:
$m_f~v_f = m_0~v_0$
$v_f = \frac{m_0~v_0}{m_f}$
$v_f = \frac{(0.20~kg)(25~m/s)}{75~kg+0.20~kg}$
$v_f = 0.0665~m/s = 6.65~cm/s$
After the man catches the ball, the man is moving with a speed of $6.65~cm/s$.
