For angles of projection of a projectile at angle (45°-θ) and (45°+θ), the horizontal ranges described by the projectile are in the ratio of

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(2) 1 : 1. Given: two launches at (45°-θ) and (45°+θ) with the same speed. Idea: the range depends on sin 2θ, and the two angles are complementary, so their doubles are supplementary. First: R₁=(u² sin [2(45°-θ)])/g=(u² sin(90°-2θ))/g=(u² cos 2θ)/g. Second: R₂=(u² sin(90°+2θ))/g=(u² cos 2θ)/g. The two are identical, so the ratio is 1:1.

For angles of projection of a projectile at angle (45°-θ) and (45°+θ), the horizontal ranges described by the projectile are in the ratio of

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