Two projectiles are launched from the ground such that their horizontal ranges are equal. The ratio of their initial speeds is 1 : 2 . If the first projectile is launched at an angle of 45^ with the horizontal, which of the following can be the angle of projection of the second projectile?

Step-by-step solution

The horizontal range of a projectile is given by R = u^2 (2 ) g . Given that the horizontal ranges are equal, we have: R₁ = R₂ u₁^2 (2 ₁) g = u₂^2 (2 ₂) g Substituting the given values u₁ u₂ = 1 2 and ₁ = 45^ : (2 ₂) = ( u₁ u₂ )^2 (2 45^ ) (2 ₂) = ( 1 2 )^2 (90^ ) (2 ₂) = 1 2 1 = 1 2 This gives 2 ₂ = 30^ or 150^ . Therefore, ₂ = 15^ or 75^ . From the given options, 15^ is the correct angle. Answer: 15^