Question

A balloon starts from rest, moves vertically upwards with an acceleration g/8 ms?. A
stone falls from the balloon after 8 s from the start. Further time taken by the stone to reach the ground (g = 9.8 ms) is​

Answer 1

$\huge {\orange {\bf {\underline {\underline {ÀnSwer}}}:-}}$

Time taken by the stone to reach the ground is 4s.

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Explaination :-

The distance of the stone above the ground about which it begins to fall from the balloon is

$\sf h = \frac{1}{2} \bigg( \frac{g}{8} \bigg) {8}^{2} = 4g$

The Velocity of the balloon at this height can be obtained from

$\hookrightarrow \sf v = u + at \\ \\ \hookrightarrow \sf v = 0 + \bigg( \frac{g}{ \cancel 8} \bigg) \cancel8 \\ \\ \hookrightarrow \sf v = 0$

This becomes the initial velocity (u) of the stone as the stone falls from the balloon at the height h.

$\therefore$u' = g

For the total motion of the stone

$\hookrightarrow \bf h = { - u}^{1} + \frac{1}{2} {gt}^{2} \\ \\ \hookrightarrow \sf - 4g = gt - \frac{1}{2} {gt}^{2} \\ \\ \hookrightarrow \sf - 4g = g(t - \frac{1}{2} {t}^{2} ) \\ \\ \hookrightarrow \sf - 4 = \frac{2t - {t}^{2} }{2} \\ \\ \hookrightarrow \sf {t}^{2} - 2t - 8 = 0 \\ \\ \hookrightarrow \sf {t}^{2} - 4t + 2t - 8 = 0 \\ \\ \hookrightarrow \sf t(t - 4) + 2(t - 4) = 0 \\ \\ \hookrightarrow \sf (t - 4)(t + 2) = 0 \\ \\ \therefore \sf t = 4 \: and \: t = - 2$

Ignore negative value of Time [ because time cannot be negative ]

Thus, te taken by the stone to reach the ground is 4s