`R` is the rangle on a horizontal planne for a shot with the same velocity at two differen angles of projection. If ` h` and `h'` be the greatest heights attained correspoinding to these angles of projection, what is ` R^2` equal to ?

Options

A. ` hh'`
B. `9 hh'`
C. ` 16 hh'`
D. ` 25 hh'`

Answer

C

Explanation

` R = u cos thea xx ( 2 u sin theta)/g = ( 2 u^2 sin theta cos theta)/g`
` R^2 = (4 u^2 sin^2 theta cos^@ theta)/g^2 ` …(i)
` h = (u^2 sin^2 theta)/(2 g) , h' = (u^2 cos ^2 theta)/(2 g)`
:. ` hh' = ( u^4 sin^2 theta cos^2 theta)/( 4 g^2) ` ....(ii)`
` From (i) and (ii) ` R^2 = 16 hh'`.