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Horizontal range for projection angle (45° − θ) is R₁ = (u² sin2(45° − θ)) / g. Horizontal range projection angle (45° + θ) is R₂ = (u² sin2(45° + θ)) / g. According to the condition, R₁ / R₂ = cos2θ / sin2θ. So, R₁ : R₂ : 1 : 1.

1. The angle of elevation (θ) of the highest point of the projectile and the angle of projection θ are related to each other as tan θ = 1 / tan θ.
2. Given, u₁ = u₂ = u, θ₁ = 60°, θ₂ = 30°.
3. Horizontal range is same when angle of projection with the horizontal is θ and (90° − θ).
4. Rmax = v² / g = 16000 [16km = 16000m].

Correct answer: Horizontal range is same when angle of projection with the horizontal is θ and (90° − θ).

Solution

The horizontal range of a projectile is the same for complementary angles of projection, i.e., θ and (90° − θ), as the sine of the angles is equal (sin2θ = sin2(90° − θ)).

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