For a given initial speed, a projectile has the same range R for two anlges of projection . If `t _(1) and t _(2)` are the times of flight in the two cases then

Options

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

Answer

B

Explanation

R is same at an angle `theta` and `(90^(@)-theta)`
`t_(1)=(2usin theta)/(g) & t_(2)=(2u sin(90-theta))/(g)=(2u cos theta)/(g)`
`t_(1)t_(2)=(2usin theta)/(g)xx(2u cos theta)/(g)=(u^(2)2 sin theta cos theta)/(g) xx(2)/(g)`
`rArr t_(1)t_(2)=(2R)/(g) rArr t_(1)t_(2)propR`