A balloon rises from rest on the ground with constant acceleration g8. A stone is dropped when the balloon has risen to a height of 39.2 m. Find the time (in s) taken by the stone to reach the ground.

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A balloon rises from rest on the ground with constant acceleration $\frac{g}{8}$ . A stone is dropped when the balloon has risen to a height of 39.2 m. Find the time (in s) taken by the stone to reach the ground.

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answer is 4.

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Detailed Solution

$v = \sqrt{2 a s} = \sqrt{2 \times \frac{g}{8} \times 39.2} = 9.8 m / s$

$39.2 = - 9.8 t + \frac{1}{2} 9.8 t^{2}$

$t^{2} - 2 t - 8 = 0$

$t = 4 s$

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