Two objects are projected at angles `30^(@)` and `60^(@)` respectively with respect to the horizontal direction. The range of two objects are denoted as `R_(30^(@))` and `R_(60^(@))`. Choose the correct relation from the following.

Options

A. `R_(30^(@)) = R_(60^(@))`
B. `R_(30^(@))= 4 R_(60^(@))`
C. `R_(30^(@))= (R_(60^(@)))/(2)`
D. `R_(30^(@)) = 2R_(60^(@))`

Answer

A

Explanation

`R_(30^(@))= R_(60^(@)) R = (u^(2) sin 2 theta)/(g)`
`(u^(2) sin 60^(@))/(g) = (u^(2))/(g) sin 120^(@)`
`(sqrt(3))/(2) = sin (90^(@) + 30^(@))`
`(sqrt(3))/(2) = cos 30^(@)`