Answer
(a) The center of mass is 5.8 meters from the woman.
(b) The distance between the man and the woman is now 4.1 meters.
(c) The man will have moved a distance of 4.2 meters.
Work Step by Step
Let $x=0$ be the point where the woman is standing initially.
(a) $x_{CM} = \frac{(72~kg)(10.0~m)}{52~kg+72~kg} = 5.8~m$
The center of mass is 5.8 meters from the woman.
(b) Since there are no net external forces on the system, the center of mass stays at rest. Therefore,
$\frac{(72~kg)(7.5~m) + (52~kg)(x_w)}{52~kg+72~kg} = 5.8~m$
$x_w = \frac{(5.8~m)(124~kg)-(72~kg)(7.5~m)}{52~kg}$
$x_w = 3.4~m$
The woman moves 3.4 meters. So the distance between the man and the woman is now (7.5 meters - 3.4 meters) which is 4.1 meters.
(c) They will meet at the center of mass. Therefore, the man will have moved a distance of (10.0 meters - 5.8 meters) which is 4.2 meters.
