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QJEEM24Ph7754: JEE Main 2024 Physics - Class 11 JEEM24Ph7754 Solution: A body starts falling freely from height hits an inclined plane …

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

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JEE Main 2024 (Online) 31st January Morning Shift Physics - Center of Mass and Collision Question 12 English Explanation

Total time of flight =T=\mathrm{T}

T=2hg+2(H−h)gT=\sqrt{\frac{2 h}{g}}+\sqrt{\frac{2(H-h)}{g}}

For max. time =dTdh=0=\frac{\mathrm{dT}}{\mathrm{dh}}=0

amp;2 g(−12H−h+12h)=0amp;H−h=hamp;h=H2⇒Hh=2\begin{aligned}& \sqrt{\frac{2}{\mathrm{~g}}}\left(\frac{-1}{2 \sqrt{\mathrm{H}-\mathrm{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\end{aligned}

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