A balloon starts from rest from the ground and moves with uniform acceleration g/8. When it reaches a height h a ball is dropped from it. Find the time taken by the ball to reach the ground.

Explanation

Velocity of balloon when it is at a height h is
`v=sqrt((2gh)/8)=sqrt(gh)/2`
`-h=vt-1/2"gt"^2`
`-h=sqrt(gh)/2 t-1/2 "gt"^2`
`1/2 "gt"^2 -sqrt(gh)/2 t-h=0`
Simplifying and taking only the positive value as negative value of t is not acceptable we get `t=2sqrt(h/g)`