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Question

A particle is projected vertically upwards from a point A on the ground. It takes t1 time to reach a point B but it still continues to move up. If it takes further t2 time to reach the ground from point B then height of point B from the ground is

A
12(t1+t2)2
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B
g t1 t2
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C
18(t1+t2)2
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D
12gt1t2
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Solution

The correct option is D 12gt1t2
Time of flight =t1+t2
s=ut112gt21 [u-initial speed, s-height of point B from ground]
At maximum height,
v=0,u=at,t=ua=ug
Time of flight =2×ug=2ug
2ug=t1+t2
u=g(t1+t2)2
s=g(t1+t2)2×t112gt21
=12gt21+12gt1t212gt21
=12gt1t2

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