Question

One-dimensional Elastic Collision.

Answer 1

Consider two bodies A and B with masses m₁ and m₂ moving with velocities u₁ and u₂ along same line in same direction. Let u₁ > u₂ . 

Suppose the bodies have velocities v₁ and v₂ after an elastic head-on collision.

Applying principle of conservation of momentum.

Solving the above equations (1) and (2); we get

u₁ - u₂ = v₂ - v₁

or velocity of approach before collision = velocity of separation after collision.

Special Cases

(i) B initially at rest i.e. u₂ = 0

i.e. the bodies exchange their velocities and momenta.