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A balloon rises from rest on the ground with an acceleration g/8. A stone is dropped from the balloon when it is at a height H. Calculate the time taken by the stone to reach the ground.

A balloon rises from rest on the ground with an acceleration g/8. A stone is dropped from the balloon when it is at a height H. Calculate the time taken by the stone to reach the ground. 

Grade:11

1 Answers

Avishek Bhagat
askIITians Faculty 67 Points
3 months ago
Dear Student,
answer to the problem is

V2= U2 + 2×g/8×H. (U = 0)

V = 1/2× √gh

Stone is released at height h with initial velocity ( - 0•5√gH)

H= Ut + 0•5gt2

H= -0•5√gHt + 0•5gt2

0•5gt2 - 0•5√gH t -H =0

t2-√H/g t - 2H/g = 0

t =( √H/g +- ✓H/g +8H/g)/2 =(√H/g +-✓9H/g)/2

t = either 2√H/g or -√H/g

negative value of time may be rejected

t =2√H/g


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