A body is thrown vertically upward with velocity `u`. The ratio of times at which it is at particular height `h` is `1 : 2`. What is the maximum height reached by the body above point of projection ?

Options

A. `(9//4)h`
B. `(4//3)h`
C. `(9//8) h`
D. none of these

Answer

C

Explanation

`H = (u^2)/(2 g)` …(i)
`(t_1)/(t_2) = (1)/(2) rArr 2t_1 = t_2` ….(ii)
`u = (1)/(2) g(t_1 + t_2)` …(iii)
`h = (1)/(2) g t_1 t_2` …(iv)
From (ii),(iii) and (iv) `u^2 = (9gh)/(4)`
Put `u^2` in equation (i) : `H = (9)/(8) h`.