A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal.

Question

A body starts falling freely from height H hits an inclined plane in its path at height h . As a result of this perfectly elastic impact, the direction of the velocity of the body becomes horizontal. The value of H h for which the body will take the maximum time to reach the ground is _____.

TestHub · Accepted Answer

Total time of flight = T can be written as, T = 2 h g + 2 H - h g For maximum time = d T d h = 0 ⇒ 2 g 1 2 h - 1 2 H - h = 0 ⇒ H - h = h ⇒ h = H 2 ⇒ H h = 2

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