Two projectile are projected with the same velocity. If one is projected at an angle of `30^(@)` to the horizontal. The ratio if maximum heights reached, is:

Options

A. `1:3`
B. `2:1`
C. `3:1`
D. `:4`

Answer

A

Explanation

If a body is projected with initial Velocity `u` at an angle `theta` with the hotizontal, then the height `H` reached by projectile is given by

`H=(u^(2)sin^(2)theta)/(2g)`
where `g` is acceleration due to gravity.
Given `theta_(1)= 30^(@)` and `theta_(2)= 60^(@)`
`:. (H_(1))/(H_(2))=(sin^(2)theta_(1))/(sin^(2)theta_(2))=(sin^(2)(30^(@)))/(sin^(2)(60^(@)))=((1/2)^(2))/((sqrt(3/2))^(2))=1/3`