For a given velocity, a projectile has the same range R for two angles of projection if `t_(1) and t_(2)` are the time of flight in the two cases then

Options

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

Answer

A

Explanation

Time to flight `t=(2usintheta)/(g)`
and Range `R=(u^(2)sin2theta)/(g)`
We get same range for angle of projection `theta` or `(90-theta)`
`t_(1)=(2usintheta)/(g),t_(2)=(2usin(90-theta))/(g)`
`t_(1)t_(2)=(4u^(2)*sinthetacostheta)/(g^(2))=(2u^(2)*sin2theta)/(gxxg)=(2)/(g)xxR`
`impliest_(1)xxt_(2)propR`.