A projectile is launched at 60 degrees with a speed of 20 m/s. What is its horizontal range neglecting air resistance (g = 9.8 m/s^2)?

A projectile is launched at 60 degrees with a speed of 20 m/s. What is its horizontal range neglecting air resistance (g = 9.8 m/s^2)?

• A. 20 m
• B. 35 m
• C. 50 m
• D. 70 m

Answer: (B)

The horizontal range of a projectile launched from level ground (ignoring air resistance) is R = v^2 sin(2θ) / g. Here v = 20 m/s and θ = 60°, so 2θ = 120° and sin(120°) = sin(60°) = √3/2 ≈ 0.866. Plugging in: R ≈ (20)^2 × 0.866 / 9.8 ≈ 400 × 0.866 / 9.8 ≈ 346.4 / 9.8 ≈ 35 m. So the range is about 35 meters.

The horizontal range of a projectile launched from level ground (ignoring air resistance) is R = v^2 sin(2θ) / g. Here v = 20 m/s and θ = 60°, so 2θ = 120° and sin(120°) = sin(60°) = √3/2 ≈ 0.866.

Plugging in: R ≈ (20)^2 × 0.866 / 9.8 ≈ 400 × 0.866 / 9.8 ≈ 346.4 / 9.8 ≈ 35 m.

So the range is about 35 meters.