Possible Momentums
Two billiard balls of equal mass are rolled in such a way that their velocities have the same magnitude but are in opposite directions.
Which of the following is an impossible outcome for the velocities of the billiard balls after a collision?
Note : Collision may or may not be elastic.
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Seen in the picture above are two possible configurations where the billiards balls could achieve the collisions in choices A and B respectively. The most important realization to make for this problem is that because the billiard balls have equal mass and opposite velocities , it must be that the momentum of the system sums to 0 . With this in mind, the momentum of the system after the collision must also sum to 0 , Since the vector sum of the velocities in both A and B sum to 0 while the vector sum of the velocities in C do not, it must be that C is impossible.