Question

A balloon starts from rest, moves vertically upwards with an acceleration $\frac{g}{8}{\text{ms}}^{-2}$. A stone falls from the balloon after $8\text{s}$ from the start. The time taken by the stone to reach the ground is $(g=9.8{\text{ms}}^{-2})$:

• A. $4s$
• B. $8s$
• C. $2$$\sqrt{2}$ s
• D. $12s$

Answer 1

Answer: (C)

$2$$\sqrt{2}$ s

For balloon, distance traveled by it in 8 sec,

$s=ut+\frac{1}{2}g{t}^2$ where $u=0$

$s$$=$$\frac{1}{2}\times \frac{g}{8}{t}^2$$=4g$

So, time taken by stone,

$s=ut+\frac{1}{2}g{t}^2$

$4g=\frac{1}{2}g{t}^2$ at this height the velocity of stone will be zero

$t^2=\sqrt{8}\Rightarrow t=2\sqrt{2}s.$