Two projectiles are fired with the same speed at complementary angles and hence have the same range R. If A₁ and A₂ are the areas under their trajectories, then:
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Two projectiles are fired with the same speed at complementary angles and hence have the same range R. If A₁ and A₂ are the areas under their trajectories, then:

G1 Physics · Accepted Answer

For a projectile, A = 2RH/3. Also H = R tanθ/4. Hence A = R²tanθ/6. For the complementary projectile, A₂ = R²cotθ/6. Therefore A₁A₂ = R⁴(tanθ cotθ)/36 = R⁴/36.