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

Answer

A

Explanation

The angle for which the ranges are same is complementary.
Let one angle be `theta , then other `90(@) - theta `
` T_(1) = (2u sin theta)/(g) , T_(2) = (2ucos theta)/(g)`
`T_(1)T_(2) = ( 4 u^(2) sin theta cos theta)/(g) = 2R (:. R = (u^(2)sin^(2)theta)/(g))` Hence it is proportional to `R`.