If the range of a gun which fires a shell with muzzle speed V is R , then the angle of elevation of the gun is

Options

A. `cos^(-1)((v^(2))/(Rg))`
B. `cos^(-1)((Rg)/(v^(2)))`
C. `(1)/(2)sin^(-1)((v^(2))/(Rg))`
D. `(1)/(2)sin^(-1)((Rg)/(v^(2)))`

Answer

D

Explanation

`R=(v^(2)sin 2 theta)/(g) rArr sin2 theta=(gR)/(v^(2))`
`rArr 2 theta=sin ^(-1)(gR)/(v^(2))rArr theta=(1)/(2)sin^(-1)(gR)/(v^(2))`