A projectile can have same range `R` for two angles of projection. It `t_1 and t_2` are the times of flight in the two cases, then what is the product of two times of flight ?

Options

A. `t_1t_2 prop R^2`
B. `t_1t_2 prop R`
C. `t_1t_2 prop 1/R`
D. `t_1t_2 prop 1/R^2`

Answer

B

Explanation

The horizontal range is the same for the angles of projection `theta` and `(90-theta)`
`t_1= (2u sin theta)/g`
`t_2=(2u sin (90^@-theta))/g=(2u cos theta)/g`
`t_1t_2=(2u sin theta)/g xx (2u cos theta)/g = 2/g [(u^2 sin 2 theta)/g]=2/g R`
where `R=(u^2 sin 2theta)/g`
Hence `t_1t_2 prop R` (as R is constant )