Projectile Motion Calculator

In short A projectile launched at 30 m/s and 45° travels 91.77 m, reaches 22.94 m at the top and is in the air for 4.33 seconds. The range is v²·sin(2θ)/g, and because sin(2θ) peaks at 2θ = 90°, the greatest distance comes from exactly 45° — but only when the projectile lands at the height it left. That condition is the part everyone forgets. Launch from 20 m up at the same 30 m/s and the best angle drops to 39.85°, because starting high rewards a flatter, faster throw that spends its speed on distance rather than on climbing. The other consequence of the same formula is that two angles adding to 90° give identical ranges: 30° and 60° both land at 79.48 m, one a high lob and the other a flat drive. That is a genuine symmetry of sin(2θ) rather than a coincidence, and it is why a mortar and a rifle can hit the same target. The whole model assumes gravity is the only force. That makes the path an exact parabola and makes the mass irrelevant — a cannonball and a pebble launched identically land together. It also means air resistance is entirely absent, which for a thrown ball is a modest error and for anything light, fast or spinning is the dominant term. Real ballistics is done numerically for exactly that reason.