The free throw
Set your release angle and speed, then shoot. The ball follows the curve Galileo described almost four hundred years ago.
Your shot. The rim is 10 feet up and about 14 feet away.
Shot 1 of 10
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Naija
MathGenesis assistant
Hi, I'm Naija, the MathGenesis assistant. I can help you find the right course, explain pricing or get your first session booked. What are you looking for?
Pick an angle and a speed, and let real projectile physics take the shot.
Set your release angle and speed, then shoot. The ball follows the curve Galileo described almost four hundred years ago.
Your shot. The rim is 10 feet up and about 14 feet away.
Shot 1 of 10
0 made
Once the ball leaves your hands, gravity is the only thing pulling on it if we ignore the air. It keeps moving forward at a steady speed while it falls faster and faster, and together those trace a parabola. Galileo worked this out in the 1600s.
Your release angle splits the speed into a forward part and an upward part, using cosine and sine from Trigonometry. Too little speed and the ball falls short, too much and it flies long. A higher arc helps because the ball drops into the rim more steeply, so the opening looks bigger from the ball's point of view.
The game runs a small physics simulation with gravity, a backboard that bounces the ball back and a soft rim. Bank shots and friendly rolls count, just like on a real court.
Every one of them runs on the math and physics we teach.
So, impressed?
Imagine what an hour a week with a patient tutor can do.