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

Answer

A

Explanation

When a particle is thrown vertically upwards with a speed u. at highest point the velocity of the particle will be zeroUsing v = u + at, we get
` " "0= u-gt " "rArr " "t= (u)/(g) " "…(i) `
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. Let ` t_1 =nt `
using `" " s= ut_1 +(1)/(2) at_1^(2) ,` we get
`rArr " "-H =u( nt) -(1)/(2) g(nt) ^(2)" "rArr " "-H =uxx n ( (u)/(g)) -(1)/(2) gn^(2)((u)/(g))^(2) " "[using (i) ]`
` rArr " "-2gH =2nu^(2) -n^(2) u^(2) rArr " "2gH =nu^(2) (n-2) `