Physics - Kinematics Question with Solution | TestHub

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,

$-h=vt-\frac{1}{2}g{t}^2$

$t=\frac{v}{g}\left[1+\sqrt{1+\frac{2gh}{v^2}}\right]$

$=\frac{\frac{\sqrt{gh}}{2}}{g}\left[1+\sqrt{1+\frac{2gh}{\frac{\mathrm{g}\mathrm{h}}{4}}}\right]$

$=\frac{2\sqrt{gh}}{g}=2\sqrt{\frac{h}{g}}$