A balloon rises from rest with a constant acceleration 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
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The velocity of balloon at height h, \(v = \sqrt{2 \left( \frac{g}{8} \right) h}\)
When the stone released from this balloon, it will go upward with velocity v = \(\frac{\sqrt{2gh}}{2}\) (Same as that of balloon). In this condition time taken by stone to reach the ground
\(t = \frac{v}{g} \left[ 1 + \sqrt{1 + \frac{2gh}{v^{2}}} \right]\) \(= \frac{\sqrt{gh/2}}{g} \left[ 1 + \sqrt{1 + \frac{2gh}{gh/2}} \right]\)
\(= \frac{2 \sqrt{gh}}{g} = 2 \sqrt{\frac{h}{g}}\)
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