I'm a bit confused regarding this question. Is it a center of mass problem or a Linear momentum one?
A cannon and a supply of cannon balls are inside a sealed railroad car. The cannon fires to the right, the car recoiling to the left. The cannon
balls remain in the car after hitting the far wall. Show that no matter how the cannon
balls are fired the railroad car cannot travel more than its length L, assuming it starts
from rest. ·

Question

I'm a bit confused regarding this question. Is it a center of mass problem or a Linear momentum one?  
A cannon and a supply of cannon balls are inside a sealed railroad car. The cannon fires to the right, the car recoiling to the left. The cannon
balls remain in the car after hitting the far wall. Show that no matter how the cannon
balls are fired the railroad car cannot travel more than its length L, assuming it starts
from rest. ·

anonymous · Answer

It looks like center of mass one. No external force is present here, so the center of mass stays where it is, which is definitely inside the car.

anonymous · Answer

Yes, no external forces are present but can the same thing can be said about Linear Momentum if I remember correctly

anonymous · Answer

Also if its a center of mass problem how can I relate the C.O.M to the max distance it could travel(its length L)

irishboy123 · Answer

answer posted on physics

start with the full displacement and see what that means for the various things in the train, and the train itself.