Question

A body falling freely from a given height H hits on inclined plane in its path at a height h. As a result of this impact the direction of the velocity of the body becomes horizontal. For what value of h/H the body will take maximum time to reach the ground?

Answer 1

height from which the ball is released from rest is H

height upto which it moves vertically downward is (H-h)

let the time upto which,the ball fall vertically diwnward be t1 and time in which it covers parbolic path be t2

using first equation of motion

t1={2(H-h)/g}^1/2

similarlly

t2=(2h/g)^1/2

T={2(H-h)/g}^1/2+{2h/g}^1/2. (adding both,to get the total time to reach the ground)

now,for maximum time,to reach the ground

dT/dH=0

On differenting it we get

h/H=1/2