Which formula gives the range of a projectile neglecting air resistance?

• A. R = v^2 / g
• B. R = v^2 sin(2θ) / g
• C. R = v g sin θ
• D. R = v cos θ / g

Answer: (B)

Range in projectile motion tells you how far the projectile travels before it lands, assuming air resistance is neglected. The horizontal speed stays constant at v cos θ, while gravity governs the vertical motion. The time the projectile is in the air comes from vertical motion: it rises and falls, giving a total time T = 2 v sin θ / g. Multiplying horizontal speed by this time yields the range: R = (v cos θ) × (2 v sin θ / g) = v^2 sin(2θ) / g. Since sin(2θ) = 2 sin θ cos θ, this form makes perfect sense for all launch angles. The maximum range occurs at θ = 45°, giving R = v^2 / g, which is why that particular value often appears, but the general expression depends on the angle through sin(2θ). The other options don’t represent a distance correctly: one omits the angle dependence, and the others have incorrect units or form.