(Momentum) Two people on a platform

[Mr. Box]

Homework Statement

Two people are standing on a 2.0-m-long platform, one at each end. The platform floats parallel to the ground on a cushion of air. One person throws a 6.0-kg ball to the other, who catches it. The ball travels horizontally. Excluding the ball, the total mass of the platform and people is 118 kg. Because of the throw, this 118-kg mass recoils. How far does it move before coming to rest again?

Homework Equations

Conservation of linear momentum:
(M1 * Vf1) + (M2 * Vf2) = (M1 *Vo1) + (M2 * Vo2)

The Attempt at a Solution

When the ball is thrown forwards, the platform should accelerate backwards because the air resistance is negligible. When the other person catches the ball the platform should move back to its original spot because the momentum of the ball is transferred to the platform, so I thought the answer was a displacement of zero, but its not. Can someone show me what wrong with my solution?

 

[NihalSh]

what you actually have to take into consideration is Center of Mass. If initially before throwing the ball, the system was at rest, then all throughout the system should be at rest in the x-direction regardless of whether the ball is moving or is caught by the other person because no external force is acting on the system in x-direction.

System includes ball+both people+platform. essentially everything on the platform

 

[Mr. Box]

I didn't even need to use linear momentum, thanks.

 

[NihalSh]

I didn't even need to use linear momentum, thanks.

yeah, true. glad to help