Projectile Motion Lab
Speed, angle, gravity — three knobs, one arc. Sweep them and find the angle that flies farthest.
Tip: fix the speed, sweep the angle from 10° to 80°, and watch the landing marker peak at 45°.
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.
Physics sticks when you have launched it yourself
This lab is one small piece of how ManySpace teaches physics — every idea as something you can launch, crash, and tune.