Motion In Two Dimensions Question 6
Question 6 - 2024 (31 Jan Shift 1)
A body starts falling freely from height $\mathrm{H}$ hits an inclined plane in its path at height $\mathrm{h}$. 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
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Answer: (2)
Solution:
Total time of flight $=\mathrm{T}$
$\mathrm{T}=\sqrt{\frac{2 \mathrm{~h}}{\mathrm{~g}}}+\sqrt{\frac{2(\mathrm{H}-\mathrm{h})}{\mathrm{g}}}$
For max. time $=\frac{\mathrm{dT}}{\mathrm{dh}}=0$
$\sqrt{\frac{2}{g}}\left(\frac{-1}{2 \sqrt{H-h}}+\frac{1}{2 \sqrt{\mathrm{h}}}\right)=0$
$\sqrt{\mathrm{H}-\mathrm{h}}=\sqrt{\mathrm{h}}$
$\mathrm{h}=\frac{\mathrm{H}}{2} \Rightarrow \frac{\mathrm{H}}{\mathrm{h}}=2$
