A balloon starts from rest,moves vertically upwards with an acceleration `g//8 ms^(-2)`.A Find the time taken by stone to reach the grounf `(g=9.8 ms^(-1))`

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,h u=0a=g/8
` h=(1)/(2)((g)/(g))8^(2)=4g`
Step-2:The velocity of the ballon at this height
can be obtained from v=u+at `V=0+((g)/(g))8=g`
This becomes the intial 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)"gt"^(2)-u^(1)t`
Here, h=4g,`u^(1)`=g,t=time of travel of stone.
`therefore -4g="gt"-(1)/(2)"gt"^(2) " "therefore-2t-8=`
Solving for .t. we get t=4 and -2s.
Ignoring negative value of time,t=4s