For a given velocity, a projectile has the same range `R` for two angles of rpojection if `t_(1)` and `t_(2)` are the times of flight in the two cases then

Options

A. `t_(1)t_(2) prop R^(2)`
B. ` t_(1)t_prop R`
C. `t_(1)t_(2) prop (1)/(R )`
D. `t_(1)t_(2) prop (1)/( R^(2))`

Answer

B

Explanation

`theta: t_(1) = (2 u sin theta)/(g)`
`(90 - theta): t_(2) = (2u sin (90 - theta))/(g) = (2u cos theta)/(g)`
`R = (u^(2))/(g).2 sin theta cos theta`
`t_(1)t_(2) = (4u^(2) sin theta cos theta)/(g^(2)) = (2)/(g).(u^(2))/(g).2 sin theta cos theta`
`= (2)/(g)R`
`t_(1)t_(2) prop R`