Two identical bodies, projected with the same speed at two different angles cover the same horizontal range R . If the time of flight of these bodies are 5 s and 10 s, respectively, then the value of R is ________ m. (Take g=10 m/s ^2 )

Step-by-step solution

For two projectiles to have the same horizontal range R with the same initial speed u , their angles of projection must be complementary, i.e., and 90^ - . The times of flight for these two angles are given by: t₁ = 2u g t₂ = 2u g Multiplying t₁ and t₂ , we get: t₁ t₂ = ( 2u g ) ( 2u g ) = 2 g ( u^2 (2 ) g ) Since the horizontal range is R = u^2 2 g , we can write: t₁ t₂ = 2R g Given t₁ = 5 s, t₂ = 10 s, and g = 10 m/s ^2 , substituting these values: 5 10 = 2R 10 50 = 2R 10 2R = 500 R = 250 m Answer: 250