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A balloon starts from rest from the grou...

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.

Text Solution

Verified by Experts

Velocity of balloon when it is at a height h is
`v=sqrt((2gh)/(8))=sqrt(gh)/(2)`
`-h=vt-(1)/(2)g t^(2)`
`-h=sqrt(gh)/(2)t-(1)/(2)g t^(2)`
`(1)/(2)g t^(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))`
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