Two projectiles are projected with the same initial velocities at the 15^ and 30^ with respect to the horizontal. The ratio of their ranges is 1:x . The value of x is:

Step-by-step solution

The horizontal range of a projectile is given by the formula R = u^2 (2 ) g . For the first projectile, the angle of projection is ₁ = 15^ . R₁ = u^2 (2 15^ ) g = u^2 (30^ ) g = u^2 2g For the second projectile, the angle of projection is ₂ = 30^ . R₂ = u^2 (2 30^ ) g = u^2 (60^ ) g = 3 u^2 2g The ratio of their ranges is: R₁ R₂ = u^2 2g 3 u^2 2g = 1 3 Given that the ratio is 1:x , we get x = 3 . Answer: 3