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 :

Options

A. `gH=(n-2)u^(2)`
B. `2gH=n^(2)u^(2)`
C. `gH=(n-2)^(2)u^(2)`
D. `2gH=nu^(2)(n-2)`

Answer

D

Explanation

Here time to reach the maximum height `t_(1)=u/g`
If `t_(2)` be the time taken to hit the ground, then
`-H=ut_(2)-1/2g t_(2)^(2)`
But `t_(2)=nt_(1)`(given)
`implies-H=u(nu)/g-1/2g(n^(2)u^(2))/g^(2)implies2gH=nu^(2)(n-2)`