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 relative between ` H, u and n` is :

Explanation

Time taken to reach the maximum height `t_(1)=(u)/(g)`
If `t_(2)` is the time taken to hit ground
i.e., `-H=ut_(2)-(1)/(2)g t^(2)`
But `t_(2)=nt_(1),So, -H=u((n u)/(g))-(1)/(2)g((n^(2)u^(2))/(g^(2)))`
`-H=(n u^(2))/(g)-(1)/(2)((n^(2)u^(2))/(g))implies2gH=n u^(2)(n-2)`