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. ` R`
B. ` 1//R`
C. ` R^2`
D. ` 1//R^2`

Answer

A

Explanation

Horizontal range is same when angle of projection is ` theta` or (90^2-theta)`
` R= ( u^2 sin 2 theta)/g , t_1 = ( 2 u sin theta )/g`
and ` t_2 = (2 u sin (90^2 - theta)/g = ( 2 u cos theta)g`
:.t_1 t_2 = ( 2 u sin theta)/g xx ( 2 u cos hteta)/g = ( 2 u^2 ( 2 sin theta cos theta)/g^2`
`= ( 2 u^2 sin 2 theta )/g = 2/g ( (u ^2 sin 2 theta)/g)`
or ` t_1 t-2 = 2/g R`
:. t-1 t_2 prop R`.