# Projectile Motion Lab

Canonical: https://manyspace.aporia.systems/tools/projectile-motion
Updated: 2026-10-13

Speed, angle, gravity — three knobs, one arc. Sweep them and find the angle that flies farthest.

## Try this

- Crown 45° yourself. Fix v₀ = 18 m/s and walk the angle from 10° to 80° in steps. The landing marker creeps out, peaks at 45°, then retreats — the sweet spot is yours now, not a memorized fact.
- Pair the complements. Try 30° and 60° at the same speed. Identical ranges, different arcs — sin(2θ) cannot tell them apart. The low arc gets there fast; the high arc gets there with style.
- Move planets. Launch at 20 m/s and 45° on Earth, then flip to the Moon. Same throw, sixfold range. Now find the Moon speed that matches your Earth distance — gravity is just a difficulty slider.

## How to read a trajectory

A projectile is two motions that ignore each other: horizontal velocity coasts forever (nothing pushes sideways), while vertical velocity loses g every second to gravity. The launch angle is the budget split — shallow keeps the speed horizontal, steep spends it on height. The arc above is that bargain drawn: every point is just “coast × time” sideways and “rise minus fall” upward.

The range formula R = v₀²·sin(2θ)/g tells the whole story. Range grows with speed squared — doubling v₀ quadruples distance — and sin(2θ) peaks exactly at θ = 45°, the perfect split between coasting and climbing. Gravity sits underneath dividing everything: the same throw on the Moon flies six times farther than on Earth.

## Related tools

- [Orbit & Gravity](https://manyspace.aporia.systems/tools/orbit)