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. `t_(1)t_(2) propR^(2)`
B. `t_(1)t_(2) prop R`
C. `t_(1)t_(2) prop1/R`
D. `t_(1)t_(2) prop1/(R^(2))`

Answer

B

Explanation

The horizontal range is the same for the angle of projection is `theta or (90^(@)- theta)`.
`t_(1)=(2u sin theta)/g`
`t_(2)=(2u sin(90^(@)- theta))/g=(2u cos theta)/g`
`t_(1)t_(2)=(2u sin theta)/gxx(2u cos theta)/g=2/g[(u^(2) sin 2theta)/g] =2/g R`
where `R=(u^(2) sin 2theta)/g` Hence `t_(1)t_(2) propR` (as R is constant)