A ball of mass 3m at speed v approaches a ball of mass 2m at speed -2v and they are about to collide.After the collision,what is the speed of the center of mass?
A) v
B) -v/5
C) v/5
D) -v
E) Can't decide because we don't know whether this collision is inelastic or elastic

Question

Quizplus · Accepted Answer

The initial momentum of the system is:
P_initial = 3m*v + 2m*(-2v) = -m*v
The final momentum must be the same, because there are no external forces acting on the system:
P_final = (3m + 2m)*v_cm
where v_cm is the velocity of the center of mass.
Using conservation of momentum:
-m*v = 5m*v_cm
v_cm = -v/5
So the answer is (C).

A Ball of Mass 3m at Speed V Approaches a Ball