When a ball undergoes a two-dimensional elastic collision with a smooth wall, the angle that the incident path makes with the perpendicular to the wall is equal to the angle that the outgoing path makes with the perpendicular to the wall
Explain why this is so.
Because the wall is smooth, it does not exert a tangential force on the ball, and the tangential component of momentum of the ball is unchanged. In the normal direction, there is a force on the ball, and it changes its momentum. In order to conserve energy, however, the magnitude of the normal component of the ball's velocity must remain unchanged. This means that that component of the velocity changes sign, and thus the two angles are equal.
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