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 abote the ground about which it begin to fall from the balloon.
`S=ut+1/2 at^(2) :" here "s=h, u=0,a=g//8`
`h=1/2 (g/8) 8^(2)=4g`
Step-2 : The velocity of the ballon 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 hte ballon at the height h.
u.=g
Step-3 : For the total motion of the stone `h=1/2 gt^(2)-u^(1)t`
Here h=4g, u.=g, t =time of the travel of stone.
`-4g=gt-1/2 gt^(2)" "t^(2)-2t-8=`
sovling for .t. we get t=4 and -2s
Ignoring negative value of time, t=4s