## Conditions on Relative Mass and Speed for a Ball to be Brought to Rest by a Collision

Suppose two balls A and B of masses m and km are moving in the same direction with speedsandrespectively, whereand 0

We can find the coefficient of restitutionin terms ofandand use the expression for e to conditions onand

Conservation of momentum gives

(1)

Ifis the coefficient of restitution between A and B, then(2)

k*(2) – (1) gives

Because e <=1, we must have

We havehenceand