Two balls are thrown with the same speed from a point `O` at the same time so that their horizontal ranges are same. If the difference of the maximum height attained by them is equal to half of the sum of the maximum heights, then the angles of projection for the balls are

Options

A. `15^(@), 75^(@)`
B. `30^(@), 60^(@)`
C. `0^(@), 90^(@)`
D. `37^(@), 53^(@)`

Answer

B

Explanation

`H_(1) = (u^(2) sin^(2) theta)/(2g), H_(2) = (u^(2) sin^(2)(90 - theta))/(2g) = (u^(2) cos^(2) theta)/(2g)`
`H_(1) - H_(2) = (1)/(2)(H_(1) + H_(2))`
`2H_(1) - 2H_(2) = H_(1) + H_(2)`
`H_(1) = 3H_(2)`
`(u^(2) sin^(2) theta)/(2g) = 3. (u^(2)cos^(2) theta)/(2g)`
`tan^(2) theta = 3 rArr tan theta = sqrt(3) rArr theta = 60^(@)`
Another angle `= 90 - theta = 30^(@)`