Question 217 of 308

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 $\dfrac{H}{h}$ for which the body will take the maximum time to reach the ground is _____.

Your answerCheck answer

Show answer and solution▾

Answer: 2

Total time of flight $=T$ can be written as,
$T=\sqrt{\dfrac{2h}{g}}+\sqrt{\dfrac{2\left(H-h\right)}{g}}$
For maximum time $=\dfrac{dT}{dh}=0$
$\Rightarrow \sqrt{\dfrac{2}{g}}\left(\dfrac{1}{2\sqrt{h}}-\dfrac{1}{2\sqrt{H-h}}\right)=0$
$\Rightarrow \sqrt{H-h}=\sqrt{h}$
$\Rightarrow h=\dfrac{H}{2} \Rightarrow \dfrac{H}{h}=2$