Perfectly Elastic Collisions:
Frame of Reference:
A frame moving with the initial velocity of the second body. This frame reduces the complexity of the problem but not its generality, since any problem could be transformed into this frame and then back again after solving the problem.
Equal Mass Objects:
Example: Billiard Balls
The moving body stops and the second body takes off with the same speed as the first body.
Light Object Collides with Heavy Object:
Example: Ball bounces off a Wall.
The light object bounces off with the same speed but in the opposite direction. The heavy object hardly moves at all.
Heavy Object Collides with Light Object:
Example: Car hitting loose gravel.
The heavy object keeps on moving at the same speed, while the light object moves off at twice the heavy body's speed. As viewed for the heavy body's frame, the light body is moving towards the heavy body with the heavy body's original speed, and it rebounds off with the same speed.