In the previous problem, if `H_(1)` and `H_(2)` are the maximum heights in the two cases, then

Options

A. `R = 2sqrt(H_(1)H_(2))`
B. `R = 4sqrt(H_(1)H_(2))`
C. `R = sqrt(H_(1)^(2) + H_(2)^(2))`
D. `R = H_(1) - H_(2)`

Answer

B

Explanation

`theta: H_(1) = (u^(2) sin^(2) theta)/(2g)`
`(90 - theta): H_(2) = (u^(2) sin^(2) (90 - theta))/(2g) = (u^(2) cos^(2) theta)/(2g)`
`R = (u^(2))/(g).2 sin theta cos theta`
`sqrt(H_(1)H_(2)) = sqrt((u^(2) sin^(2) theta)/(2g).(u^(2) cos^(2) theta)/(2g))`
`= (u^(2) sin theta cos theta)/(2 g) = (1)/(4) ((u^(2))/(g).2 sin theta cos theta)`
`= (1)/(4)R`
`R = 4sqrt(H_(1)H_(2))`