A balloon starts from rest, moves vertically upwards with an acceleration `g/8 "ms"^(-2)`. A stone falls from the balloon after 8s from the start. Find the time taken by the stone to reach the ground `(g=9.8 ms^(-2))`

Explanation

Step-1 : To find the distance of the stone above the ground about which it begins to fall from the balloon.
`S=ut+1/2at^2`, here , s=h , u=0 , a=g/8
`h=1/2(g/8)8^2=4g`
Step-2 : The velocity of the balloon at this height can be obtained from v=u+at
`V=0+(g/8)8=g`
This becomes the initial velocity `(u^"|")`of the stone as the stone falls from the balloon at the height h.
`therefore u^("|")=g`
Step-3 : For the total motion of the stone `h=1/2 g t^2-u^("|")t`
Here, h=4g, `u^("|")`=g, t=time of travel of stone .
`therefore -4g=g t -1/2 g t^2`
`therefore t^2-2t-8=0`
solving for .t. we get t=4 and -2s
Ignoring negative value of time , t=4s