A projectile can have the same range 'R' for two angles of projection . If `'T_(1)'` and `'T_(2)'` to be times of flights in the two cases, then the product of the two times of flights is directly proportional to .

Options

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

Answer

C

Explanation

A projectile can have same range if angles of projection are complementray i.e. `theta` and `(90^(@)- theta)`. Thus, in both cases.
`t_(1)=(2u sin theta)/g`
`t_(2)=(2u sin(90^(@)- theta))/g`
`=(2u cos theta)/g`
From eq (i) and (ii)
`t_(1)t_(2)=(4 usin theta cos theta)/(g^(2))`
`=(2u^(2) sin 2 theta)/(g^(2))`
`:. t_(1)t_(2)=(2R)/(g) ( :. R =(u^(2) sin 2 theta)/g)`
Hence `t_(1)t_(2) prop R`