Question

A body dropped from a height H above the ground strikes an inclined plane at a height $h$ above the ground. As a result of the impact, the velocity of the body becomes horizontal. The body will take the maximum time to reach the ground if

• A. $h=\frac{H}{4}$
• B. $h=\frac{H}{2\sqrt{2}}$
• C. $h=\frac{H}{2}$
• D. $h=\frac{H}{\sqrt{2}}$

Answer 1

Answer: (C)

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

$T_1=$ Time taken to $H-h\Rightarrow \frac{\sqrt{2(H-h)}}{g}$
$T_2=$ Remaining $h=\sqrt{2h/g}$
$T=T_1+T_2=\frac{\sqrt{\left(2\right(H-h)}}{g}+\frac{\sqrt{2h}}{g}$
$\frac{dt}{dh}=0whenh=\frac{H}{2}$
Therefore T is maximum when $h=H/2$