Question

prove that for an elastic collision coefficient of restitution is=1

Answer 1

The coefficient of restitution e is a measure of the elasticity in a one-dimensional collision.* Its origin arises from the fact that during a perfectly elastic collision of two bodies, the velocity of approach is always equal to the velocity of separation, so that e = 1 in elastic collisions. In a perfectly inelastic collision the velocity of separation is zero, so that e = 0 in a totally inelastic collisions. 
Type 
Kinetic Energy 
Restitution 
Perfectly Elastic 
Conserved 
e = 1 
Partially Elastic 
Not Conserved 
0 < e < 1