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From a tower of height H, a particle is ...

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 that taken by it to reach the highest point of its path. The relation between H, u and n is:

A

gH = `(n - 2)u^(2)`

B

2 gH = `n^(2)u^(2)`

C

gH = `(n - 2)^(2)u^(2)`

D

2 gH = `nu^(2)(n - 2)`

Text Solution

Verified by Experts

The correct Answer is:
(d)
Time taken by the particle to reach the top most point is,
`t = u/g` . ..(i)
Time taken by the particle to reach the ground = nt
Using, `s = ut + 1/2 at^(2)`
`implies -H = u(nt) - 1/2 g(nt)^(2)`
`implies -H = u xx n(u/g) - 1/2 gn^(2)(u/g)^(2)` [using (i)]
`implies -2gH = 2nu^(2) - n^(2)u^(2) implies 2gH = nu^(2)(n - 2)`
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