#### Sample Problem: Direct impact: Two spheres moving in opposite directions

Two smooth spheres of masses *m* and 4*m* collide directly when moving in opposite directions with speeds *u* and *v* respectively. (See Fig. 1). The sphere of mass 4*m* is brought to rest by the impact. Prove that where *e *is the coefficient of restitution. (Note: masses are in kg, speeds are in m/s)

#### Solution

The next step is to identify the motion of the particles before and after the collision and express this in mathematical equations:

We have:

From the Principle of Conservation of Linear Momentum: