A projectile is launched from ground level with speed 20 m/s at 30° above the horizontal. Ignoring air resistance, what is its horizontal range?

A projectile is launched from ground level with speed 20 m/s at 30° above the horizontal. Ignoring air resistance, what is its horizontal range?

• A. Approximately 24 m
• B. Approximately 35 m
• C. Approximately 50 m
• D. Approximately 70 m

Answer: (B)

Horizontal range on level ground with no air resistance comes from how fast you launch and at what angle. The range depends on v^2 and the sine of twice the angle: R = v^2 sin(2θ) / g. Here, v = 20 m/s and θ = 30°, so 2θ = 60° and sin(60°) ≈ 0.866. Plugging in gives R ≈ (20^2)(0.866)/9.8 = 400 × 0.866 / 9.8 ≈ 346.4 / 9.8 ≈ 35 m. So the projectile travels about 35 meters before landing. This fits with the fact that the maximum range for this speed occurs at 45° and is about 40.8 m, so 30° gives a range a bit less than that. The other numbers don’t match these calculations.

Horizontal range on level ground with no air resistance comes from how fast you launch and at what angle. The range depends on v^2 and the sine of twice the angle: R = v^2 sin(2θ) / g.

Here, v = 20 m/s and θ = 30°, so 2θ = 60° and sin(60°) ≈ 0.866. Plugging in gives R ≈ (20^2)(0.866)/9.8 = 400 × 0.866 / 9.8 ≈ 346.4 / 9.8 ≈ 35 m.

So the projectile travels about 35 meters before landing. This fits with the fact that the maximum range for this speed occurs at 45° and is about 40.8 m, so 30° gives a range a bit less than that. The other numbers don’t match these calculations.