When a ball strikes a wall at right angles with a speedit will rebound with a speedwhereis the coefficient of restitution between the ball and the wall.
In general however the ball will not strike the wall at right angles, but at some glancing angle, as shown below.
In this case the speed of the ball after the collision is notWe can use the principle of restitution, which statesresolvingperpendicular and parallel to the wall. The approach and separation speeds are the components ofperpendicular to the wall before and after the collision, as shown below.
The approach speed before the collision isand the separation speed after the collision is The principle of restitution gives
The components of the velocities parallel to the wall are unchanged, since the impulse received by the ball is perpendicular to the wall, so thatThe kinetic energy of the ball after the collision is not thenas for the head on collisions, but