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Projectile motion (no air resistance): angle for maximum horizontal range A projectile is launched with a given speed. At what angle of projection is the range greatest?

Q: Projectile motion (no air resistance): angle for maximum horizontal range A projectile is launched with a given speed. At what angle of projection is the range greatest?

Given data Projectile launched with speed u; no air resistance; flat ground. Concept/Approach Range R = (u2/g)·sin 2θ. R is maximized when sin 2θ = 1. Step-by-step sin 2θ = 1 → 2θ = 90° → θ = 45°. Final Answer 45°

Difficulty: Easy

30°
45°
60°
90°
0°

Correct Answer: 45°

Explanation:

Given data

Projectile launched with speed u; no air resistance; flat ground.

Concept/Approach

Range R = (u²/g)·sin 2θ. R is maximized when sin 2θ = 1.

Step-by-step
sin 2θ = 1 → 2θ = 90° → θ = 45°.

Final Answer
45°

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