Two stones having different masses `m_(1)` and `m_(2)` are projected at an angle `alpha` and `(90^(@) - alpha)` with same speed from same point. The ratio of their maximum heights is

Options

A. `1:1`
B. `1: tan alpha`
C. `tan alpha :1`
D. `tan^(2) alpha :1`

Answer

D

Explanation

Maximum height, `H = (u^(2) sin^(2) alpha)/(2g) rArr H prop sin^(2) alpha`
`:. (H_(1))/(H_(2)) = (sin^(2)alpha)/(sin^(2)(90^(@)-alpha)) = tan^(2) alpha`