Conservation of linear Momentum Theory

[Speedking96]

Homework Statement

You are standing on your skateboard, which is at rest. Your friend throws a heavy ball at you. What should you do to minimize your velocity?

A. Catch the ball
B. Hit the ball back with the same velocity
C. Neither, they both have the same effect.

I would say (A). Because if I were to hit the ball, then I would have to provide a greater force to get it going back in the other direction, this would create a larger reaction force on me, which would give me even more momentum.

Is this correct?

 

[gneill]

You're correct but not quite for the right reason. What you have to consider is conservation of momentum. Reaction forces can be large or small depending upon the time over which they occur, but momentum is ALWAYS conserved.

If you start out stationary then your momentum is zero and the ball moving towards you has all the momentum of the "system" that comprises you and the ball. Remember that momentum is a vector quantity! The momentum of the system must retain that same magnitude and direction. Think about how that can be true if you (a) catch the ball, and (b) hit it back. What does it imply for your eventual velocity in each case?