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

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Solution

Q.
A body starts falling freely from height $H$ and 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 ______. [2024]

Ans.
(2)

Total time of flight = T

$T = \sqrt{\frac{2 h}{g}} + \sqrt{\frac{2 (H - h)}{g}}$

For maximum time $= \frac{d T}{d h} = 0$

$\sqrt{\frac{2}{g}} (\frac{- 1}{2 \sqrt{H - h}} + \frac{1}{2 \sqrt{h}}) = 0$

$\sqrt{H - h} = \sqrt{h}$

$h = \frac{H}{2} \Rightarrow \frac{H}{h} = 2$

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