Two projectiles are thrown from the ground with the same initial speed. The first projectile is launched at an angle that yields the maximum possible horizontal range. The second projectile is launched at an angle of 15^ with the horizontal. If the horizontal range of the first projectile is R₁ and that of the second projectile is R₂ , find the value of R₁ R₂ .

Step-by-step solution

The horizontal range of a projectile is given by R = u^2 (2 ) g . For the first projectile, the range is maximum. This occurs when the angle of projection is 45^ . Thus, R₁ = u^2 (90^ ) g = u^2 g . For the second projectile, the angle of projection is 15^ . Thus, R₂ = u^2 (2 15^ ) g = u^2 (30^ ) g = u^2 2g . Taking the ratio of the two ranges: R₁ R₂ = u^2 g u^2 2g = 2 . Answer: 2