Question

A ball falls from a height of 1 m,hits the ground and rebounds with half its velocity just before impact ,Then after raising it falls and hits the ground and again rebounds with half its velocity just before impact and so on .The total distance traveled by ball till it comes to rest is ______

Answer 1

Hints:
Half the velocity means 1/4 of the kinetic energy, hence the heights reached in successive bounces is 1/4 of the previous height.
If we have a geometric progression with common ratio r, the sum to infinity is
a0/(1-r) where a0 is the initial value.
Note that between bounces, the ball travels twice the maximum height reached.