How far does a platform recoil when someone throws a ball across it?

[Parzival]

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, like a hovercraft. one person throws a 6.0 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 118 kg. Because of the throw, this 118 kg mass recoils. How far does it move before coming to rest again?

Homework Equations

Momentum after = momentum before

The Attempt at a Solution

I realized that conservation of momentum applied, but I couldn't set up any equations.

 

[TSny]

You might consider approaching this problem by thinking about what happens to the position of the center of mass of the entire system.

 

[zzinfinity]

Do you know the velocity with which the ball was thrown?

 

[Parzival]

You might consider approaching this problem by thinking about what happens to the position of the center of mass of the entire system.

May you please clarify? I've been stumped for a long time.

 

[TSny]

Take the system to consist of the platform, the two people, and the ball. There are no external forces acting horizontally on the system. So, the center of mass of the system relative to the ground will remain in the same place.

Suppose the person on the left end of the platform initially holds the ball. Where would the center of mass of the system be relative to the center of the platform? When the person on the right has the ball, where is the center of mass of the system relative to the center of the platform? From this, try to see how far the platform must move in order to keep the center of mass at the same location relative to the ground.