A ball of mass `m` is thrown vertically upwards. Another ball of same mass is thrown at an angle `theta` to the horizontal. If the time if flights for both is same, the ratio of maximum height attained by them

Options

A. `1 : 2`
B. `1 : sin^(2)theta`
C. `1 : 1`
D. `cos^(2) theta : 1`

Answer

C

Explanation

`T_(1) = (2 u_(1))/(g), T_(2) = (2 u_(2) sin theta)/(g)`
`T_(1) = T_(2) rArr u_(1) = u_(2) sin theta`
`((H_(1))_(max))/((H_(2))_(max)) = (u_(1)^(2)//2g)/(u_(2)^(2) sin^(2) theta//2g) = (1)/(1)`