Question

A balloon rises from rest with a constant acceleration of $\frac{g}{8}$ . A stone is released from it when it has risen to height $h$ . The time taken by the stone to reach the ground is $n\sqrt{\frac{h}{g}}$ seconds. Then what is the value of $n$ ?

Answer 1

From equation $v^{2}=u^{2}+2as$
Given, $u=0,a=\frac{g}{8}$
$\therefore $ We have, $v=\sqrt{2 \left(\frac{g}{8}\right) h}$
When the stone released from this balloon. It will go upward with velocity $v=\sqrt{g h}$
In this condition, time taken by stone to reach the ground,
$- h = v t - \frac{1}{2} g t^{2}$
$t=\frac{v}{g}\left[1 + \sqrt{1 + \frac{2 g h}{v^{2}}}\right]$
$=\frac{\frac{\sqrt{g h}}{2}}{g}\left[1 + \sqrt{1 + \frac{2 g h}{\frac{g h}{4}}}\right]$
$=\frac{2 \sqrt{g h}}{g}=2\sqrt{\frac{h}{g}}$