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

Answer

D

Explanation

A projectile can have same range if angles of projection are complementary ie, `theta` and `(90^@ - theta)`
In both cases
`t_1 = (2u sin theta)/(g)`…(i)
`t_2 = (2 u sin(90^@ - theta))/(g)`
=`(2 u cos theta)/(g)` …(ii)
From Eqs. (i) and (ii)
`t_1 t_2 = (4 u^2 sin theta cos theta)/(g^2)`
`t_1 t_2 = (2 u^2 sin 2 theta)/(g^2)`
=`(2)/(g) (u^2 sin 2 theta)/(g)`
`:. t_1 t_2 = (2 R)/(g)` `(because R = (u^2 sin 2 theta)/(g))`
Hence, `t_1 t_2 prop R`.