Answer
(a) The person and the ball move with a speed of 8.50 cm/s.
(b) The person's speed is 0.154 m/s.
Work Step by Step
We can find the initial momentum.
$p = mv = (0.600~kg)(10.0~m/s)$
$p = 6.00~kg~m/s$
(a) Let $M$ be the total mass.
$Mv = p$
$v = \frac{p}{M} = \frac{6.00~kg~m/s}{70.0~kg+0.600~kg}$
$v = 0.0850~m/s = 8.50~cm/s$
The person and the ball move with a speed of 8.50 cm/s.
(b) Let $p_p$ be the person's momentum and let $p_b$ be the ball's momentum after the collision.
$p_p+p_b = p$
$p_p = p - p_b$
$m_pv_p= p - m_bv_b$
$v_p= \frac{p - m_bv_b}{m_p}$
$v_p= \frac{6.00~kg~m/s- (0.600~kg)(-8.0~m/s)}{70.0~kg}$
$v_p = 0.154~m/s$
The person's speed is 0.154 m/s.
