Two particles are projected with same initial velocity one makes angle `theta` with horizontal while other makes an angle `theta` with vertical. If their common range is R then product of their time of flight is directly proportional to :

Options

A. R
B. `R^2`
C. `1/R`
D. `R^0`

Answer

A

Explanation

`R=(u^2sin2theta)/(g), t_1=(2usintheta)/(g)`
`t_2 = (2usin(90^@-theta))/(g)=(2ucostheta)/(g)`
`therefore" " t_1t_2=(4u^2sinthetacostheta)/(g)=(2R)/(g)`
`or" "t_1t_2propR`