Motion In Two Dimensions Question 6
Question 6 - 2024 (31 Jan Shift 1)
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 $\frac{H}{h}$ for which the body will take the maximum time to reach the ground is
Show Answer
Answer: (2)
Solution:
Total time of flight $=T$
$T=\sqrt{\frac{2 h}{g}}+\sqrt{\frac{2(H-h)}{g}}$
For max. time $=\frac{dT}{dh}=0$
$\sqrt{\frac{2}{g}}\left(\frac{-1}{2 \sqrt{H-h}}+\frac{1}{2 \sqrt{h}}\right)=0$
$\sqrt{H-h}=\sqrt{h}$
$h=\frac{H}{2} \Rightarrow \frac{H}{h}=2$
