Two bodies are projected with the same velocity. If one is projected at an angle of 30^ and the other at 45^ to the horizontal, then the ratio of maximum heights attained is

Step-by-step solution

The maximum height attained by a projectile is given by H = u^2 ^2 2g . For the first body, ₁ = 30^ : H₁ = u^2 ^2 30^ 2g = u^2 2g ( 1 2 )^2 = u^2 8g For the second body, ₂ = 45^ : H₂ = u^2 ^2 45^ 2g = u^2 2g ( 1 2 )^2 = u^2 4g The ratio of maximum heights is: H₁ H₂ = u^2 8g u^2 4g = 4 8 = 1 2 Thus, the ratio is 1:2 . Answer: 1:2