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Question

A stone dropped from the top of a building of height h. It reaches the ground after t s. From the same building if two stones are thrown (one upwards and other downwards) with the same velocity u, and they reach the earth surface after t1 and t2 seconds respectively, then


A

t=t1t2

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B

t=t1+t22

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C

t=t1t2

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D

t=t21t22

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Solution

The correct option is C

t=t1t2


If a stone is dropped from a height h then

h=12gt2 .....(i)

If a stone is thrown upward with velocity u then

h=ut1+12gt21 ........(ii)

If a stone is thrown downward with velocity u then

h=ut2+12gt22 ............(iii)

From (i)(ii) and (iii) we get

ut1+12gt21=12gt2 .................(iv)

ut2+12gt22=12gt2 ..................(v)

Dividing (iv) and (v) we get

ut1ut2=12g(t2t21)12g(t2t22) or t1t2=t2t21t2t22

By solving t=t1t2


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