Question

A ball which is at rest is dropped from height $h$ metre. As it bounces off the floor, its speed is $80$% of what it was just before touching the ground. The ball will then rise to nearly a height.

• A. $0.94h$
• B. $0.74h$
  
• C. $0.64h$
  
• D. $0.84h$
  

Answer 1

The correct option is C $0.64h$

Since the speed of the ball after first collision becomes $80$% of its speed just before touching the ground.

Thus we get coefficient of restitution $e=0.8$

Initial height from which the ball is dropped $h_i=h$

Thus the height to which the ball will rebound after first collision is given by $h_f=e^2{h}_i$

$\therefore h_f=(0.8{)}^2\times h=0.64h$