Two projectiles are fired from the same point at height h above horizontal ground with the same speed u. Their angles of projection are θ and 90°-θ.They strike the ground with velocity directions making equal angles with the horizontal. For h>0, which conclusion is necessary?
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Question

Two projectiles are fired from the same point at height h above horizontal ground with the same speed u. Their angles of projection are θ and 90°-θ.They strike the ground with velocity directions making equal angles with the horizontal. For h>0, which conclusion is necessary?

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G1 Physics · Accepted Answer

For projection at angle θ, tanφ₁ = √(u²sin²θ+2gh)/(u cosθ). For projection at 90°-θ, tanφ₂ = √(u²cos²θ+2gh)/(u sinθ). Equal impact angles imply tanφ₁ = tanφ₂. Squaring, sin²θ[u²sin²θ+2gh] = cos²θ[u²cos²θ+2gh]. Rearranging, (sin²θ-cos²θ) [u²(sin²θ+cos²θ)+2gh] = 0. The second bracket is strictly positive, so sin²θ = cos²θ. Therefore, θ = 45°.

Two projectiles are fired from the same point at height h above horizontal ground with the same speed u. Their angles of projection are θ and 90°-θ.They strike the ground with velocity directions making equal angles with the horizontal. For h&gt;0, which conclusion is necessary?

Two projectiles are fired from the same point at height h above horizontal ground with the same speed u. Their angles of projection are θ and 90°-θ.They strike the ground with velocity directions making equal angles with the horizontal. For h>0, which conclusion is necessary?