Two objects are projected with same velocity 'u' at different angles and with the horizontal. If + = 90^ , the ratio of horizontal range of the first object to the second object will be [ ( - ) = ]

Step-by-step solution

The horizontal range of a projectile is given by R = u^2 (2 ) g . For the first object projected at angle , the range is R₁ = u^2 (2 ) g . For the second object projected at angle , the range is R₂ = u^2 (2 ) g . Given + = 90^ , we have = 90^ - . Substituting in the expression for R₂ : R₂ = u^2 (2(90^ - )) g = u^2 (180^ - 2 ) g Using the identity (180^ - ) = , we get: R₂ = u^2 (2 ) g Thus, R₁ = R₂ , which means the ratio of their horizontal ranges is 1 : 1 . Answer: 1 : 1