Projectile Motion: Range, peak height and flight time for any launch speed, angle and gravity. This free calculator solves for Range, max height, flight time and shows every step.
Horizontal and vertical motion are completely independent. Horizontal velocity stays constant (no horizontal force), while vertical velocity changes at a steady g. Constant horizontal displacement combined with accelerating vertical displacement traces a parabola. On flat ground the range is greatest at θ = 45°; with air resistance the optimum drops to roughly 38–42°. In the ideal drag-free model, mass cancels out — a feather and a cannonball follow the same path.
Launch at v₀ = 20 m/s, θ = 45°, flat ground, Earth.
R = 20²·sin90° / 9.81 = 400 / 9.81 = 40.8 m; H = (20·sin45°)² / (2·9.81) = 10.2 m; t = 2·(20·sin45°)/9.81 = 2.88 s.
Ballistics, sport (basketball arcs, golf, javelin, long jump), water-jet fountains, fireworks — any "launch and land" trajectory problem.
Projectile Motion uses the formula R = v₀²·sin(2θ) / g. Range, peak height and flight time for any launch speed, angle and gravity.
Choose which variable to solve for, enter the values you know (in any supported unit), and the calculator substitutes them into R = v₀²·sin(2θ) / g and shows every step of the working. It can solve for Range, max height, flight time.
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