BACKBOARD
The free-throw cage, run by a crew member with a very long arm. Angle sweeps, you lock it, then speed sweeps and you lock that. Every basket pays tickets — and the readout tells you the physics you just used.
What this machine is actually teaching
Every shot is projectile motion. Once the ball leaves your hands only two things decide where it lands: the angle you launched it at and how fast it was going. Gravity does the rest, the same way every time.
The range of a throw follows R = v² · sin(2θ) / g. Because of that sin(2θ), 45° throws the furthest for a given speed — and every distance short of maximum can be reached two ways: a flat fast arc, or a high floaty one. Watch the dotted line: 30° and 60° land in the same place.
Which one should you pick? The high arc drops more steeply into the hoop, so it has a bigger target to fall through — which is exactly why real free throws are shot high, not flat.