Two spheres are projected at angles 30^ and 45^ with the horizontal. The maximum height reached by both is same. The ratio of their initial velocities is, ( 45^ = 1 2 , 30^ = 0.5 )

Step-by-step solution

The maximum height reached by a projectile is given by H = u^2 ^2 2g Given that the maximum heights are equal for both spheres: H₁ = H₂ u₁^2 ^2 ₁ 2g = u₂^2 ^2 ₂ 2g u₁ ₁ = u₂ ₂ Substituting ₁ = 30^ and ₂ = 45^ : u₁ 30^ = u₂ 45^ u₁ ( 1 2 ) = u₂ ( 1 2 ) u₁ u₂ = 2 2 = 2 1 The ratio of their initial velocities is 2 : 1 . Answer: 2 : 1