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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

` 2 g H = n^(2) u^(2)`

B

` g H = ( n - 2) ^(2) u^(2)`

C

` 2 g H = n u ^(2) ( n - 2)`

D

` g H = (n - 2) u^(2)`

Text Solution

Verified by Experts

The correct Answer is:
C
Time to reach the maximum height
`t_(1) = (u)/( g)`
it ` t_(2)` be the time taken to hit the ground
` - H = ut _(2) - (1)/(2) g t _(2)^(2)`
`t_(2) = nt_(1)`
`rArr - H = u ( nu)/( g) - (1)/(2) h "" ( n^(2) u^(2))/( g^(2)) = (nu^(2))/( g) - (n^(2) u^(2))/( 2 g)`
`rArr 2 gH = nu ^(2) ( n - 2)`
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