From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the particle to hit the ground is n times the time taken by it to reach the highest point of its path. The relation between H, u and n is
A
2gH=n2u2
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B
gH=(n−2)2u2
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C
2gH=nu2(n−2)
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D
2gH=(n−2)2u2
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Solution
The correct option is C2gH=nu2(n−2) Let t1 and t2 be the time taken by the particle to reach maximum height and ground respectively. Since final velocity will be zero when particle reaches maximum height, therefore time taken to reach maximum height, t1=ug
Using second equation of motion, we can say −H=ut2−12gt22(1) t2=n×t1(2) Using (2) in (1), we get −H=unug−12gn2u2g2 ⟹−H=2nu2−n2u22g ∴2gH=nu2(n−2)