Proof That Relative Speed is Conserved in Elastic Collisions

Kinetic energy is conserved in elasic collisions, and momentum is always conserved. To prove that relative speed is conserved suppose that masseshave initial velocitiesfinal velocitiesso initial speedsand final speedsa

Then conservation of kinetic energy implies

(1)

Conservation of momentum implies (2)

From (1) (3)

From (2)

Hence

Thenand relative speed is conserved.