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

Answer: 2

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 $v=\sqrt{gh}$
In this condition, time taken by stone to reach the ground,
$-h=vt-\frac{1}{2}g{t}^2$
$t=\frac{v}{g}\left[1+\sqrt{1+\frac{2gh}{v^2}}\right]$
$=\frac{\frac{\sqrt{gh}}{2}}{g}\left[1+\sqrt{1+\frac{2gh}{\frac{gh}{4}}}\right]$
$=\frac{2\sqrt{gh}}{g}=2\sqrt{\frac{h}{g}}$