Question

A racquetball (diameter 8.00 cm, mass 60.0 g) is held a negligible distance above a basketball (diameter 30.0cm, mass 610. g). The bottom of the basketball is 4.00 m above a hard floor e.g. at the height of the second-floor railing of the physics building. The two balls are dropped together from rest. The basketball bounces off the floor and strikes the racquetball. All collisions have 0.700 coefficient of restitution. Neglecting aerodynamic effects, calculate the height to which the racquetball would rebound, if the ceiling is not an obstacle.

Answer 1

Taking downward velocities negative

The velocity of the basketball and racquetball just before it collides with the floor

The velocity of the basketball after this collision

The total momentum of the system after this collision

Total momentum after the collision between the two balls

Conservation of the momentum gives us

................ (1)

Restitution gives us

Putting this in equation 1

The kinetic energy due to this velocity

At maximum height, all the kinetic energy is converted to potential energy. So,

So the maximum height of the racquetball is 10.63 m.