A ballon rises from rest with a constant acceleration g/8. A stone is released

A ballon rises from rest with a constant acceleration g/8. A stone is released from it when it has risen to height h.The time taken by the stone to reach the ground is

Options

(a) 4√(h/g)
(b) 2√(h/g)
(c) √(2h/g)
(d) √(g/h)

Correct Answer:

2√(h/g)

Explanation:

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  • The velocity of the balloon at the height h is
    v = √(2ah) = √(2gh/8) = √(gh)/2

    Initial velocity of the stone at height h is u = √(gh)/2 upwards
    h = ut + gt²/2
    put the value of u in the above relation and rearrange the terms to obtain,
    (√(gH)/2 )t  + gt²/2 - h = 0

    (√(gH))t  + gt² - 2h = 0

    The time taken by the stone to reach the ground can be obtained by solving the above quadratic.

    t = 2√[h/g]

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