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`
B. `t_1 t_2 prop R^2`
C. `t_2t_2 prop 1/(R^2)`
D. `t_1t_2 prop 1/R`

Answer

A

Explanation

`t_1 = (2u sin alpha)/(g)`
`t_2 = (2 u sin (90^@ - alpha))/(g)`
So `t_1 xx t_2 = 2 (u^2)/(g^2) sin 2 alpha`
or `t_1 xx t_2 = (2R)/(g) " " (because R = (u^2 sin alpha)/(g))`
`t_1 xx t_2 prop R`