A particle is projected at such an angle that the horizontal range is three times the greates height attained. For this situation which one of the following statements is correct ?

Options

A. The angle of projection is `25^(@) 8'`
B. The angle of projection is `54^(@) 1'`
C. The angle of projection is `53^(@) 1'`
D. The angle of projection is `32.7^(@) `

Answer

C

Explanation

Greatest height ` h_("max") = (u^(2) sin ^(2) theta)/(2g)`
Horizontal range `R = (u^(2) sin 2 theta)/(g)`
Given : `R = 3 h_("max")`
`(u^(2) sin 2 theta)/(g) = 3 xx (u^(2) sin^(2) theta)/(2g)`
`(2 sin theta cos theta)/(g) = (3 sin^(2) theta)/(2g)`
`2 cos theta = (3)/(2) sin theta`
`:. 3 sin theta = 4 cos theta`
`(sin theta)/(cos theta) = (4)/(3)`
`:. tan theta = (4)/(3)`
`:. theta = tan ^(-1) ((4)/(3))`
`theta = 53 . 1^(@)`