Two bodies are projected from ground with same speeds 40 m s - 1 at two different angles with respect to horizontal. The bodies were found to have same range. If one of the body was projected at an angle of 60 ° , with horizontal then sum of the maximum heights, attained by the two projectiles, is _____ m . (Given g = 10 m s - 2 )

Step-by-step solution

For two projectiles with same speed to have the same horizontal range, angle of projection will be θ 1 + θ 2 = 90 ° . Therefore, θ 2 = 90 ° - 60 ° = 30 ° . Now, required sum of maximum heights will be, H max 1 + H max 2 = u 2 sin 2 θ 1 2 g + u 2 sin 2 θ 2 2 g = 40 2 20 1 4 + 3 4 = 80   m