A balloon starts from rest, moves vertically upwards with an acceleration `g//8ms^(-2)`. A stone falls from the balloon after 8s from the start. Find the time taken by the stone to reach the ground `(g=9.8ms^(-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)/(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 balloon at this height can be obtained from `v=u+at`
`V=0+((g)/(8))8=g`
This becomes the initial velocity `(u^(1))` of the stone as the stone falls from the balloon at the height h.
`therefore u^(1)=g`
Step-3 : For the total motion of the stone `h=(1)/(2)g t^(2)-u^(1)t`
Here, `h=4g,u^(1)=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`.