Question

A ball with mass m move with speed v as it collides with a stationary ball with mass 2m. After the collision the first ball bounces off in the opposite direction at v/sqrt(2) of its initial speed.Find the velocity of the second ball (mass 2m) immediately after the collision.

Answer 1

From the conservation of momentum:

$$mv=2mV-mv\frac{1}{\sqrt{2}}$$

$$v+v\frac{1}{\sqrt{2}}=2V$$

The  velocity of the second ball (mass 2m) immediately after the collision:

$$V=\frac{v}{2}\left(1+\frac{1}{\sqrt{2}}\right)$$