Because there are no external horizontal forces, the center of mass of board + people + ball remains in the same place. Since the ball moves from one end to the other, the board and people on it must recoil in the opposite direction. Motion stops when the ball is caught.
Use those facts to calculate the motion.
Two people are standing on a 2.2-m-long platform, one at each end. The platform floats parallel to the ground on a cushion of air, like a hovercraft. One person throws a 6.1-kg ball to the other, who catches it. The ball travels nearly horizontally. Excluding the ball, the total mass of the platform and people is 124 kg. Because of the throw, this 124-kg mass recoils. How far does it move before coming to rest again?
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