A ball of mass m moves towards a ball of mass km with speed u. The coefficient of restitution is 0. What is the final velocity if the first ball after the collision.

Coefficient of restitution is defined as the ratio of the relative speed of separation of the balls to the relative speed of approach. A ratio of 0 means that the speed of separation has a value of zero as the speed of approach is u, therefore the balls coalesce after the collision. Because the balls and surface are smooth, no external forces act upon the balls which means linear momentum is conserved. Let us define v as the final velocity of the balls.mu = v(m+km) therefore v = u/(1+k)