Basketball and the Jump Shot

Countless great shooters have gone through the NBA, Ray Allen, Steph Curry, Steve Kerr, Jerry West, the list goes on and on. But what did they all have in common? They were great at physics! (maybe)
Regardless of their grade in high school physics, these shooters have made their living by putting a ball in a hoop from great distances. So what are these players doing that other players are not? Well first of all, like anything shooting takes a lot of practice! But there are ways to maximize your shooting percentage using physics. In general, the physics of the jump shot revolves around projectile motion and kinematics.
Let's assume a shooter has stopped on the three point line and is about to take the a shot. What does F=MA (Newton's second law) have to do with this? All of the forces that are acting on the ball and the ball's constant mass are what determine how fast that ball is going to travel. This seems fairly intuitive, but many shooters aren't sure where all these forces are coming from. The force acting on the ball is the culmination of the shooters legs from the jump, his arms from shot, and his wrist from the release.

Projectile Kinematics
Once the shot is released, it no longer has any forces acting on it (not including air resistance) except for gravity. This means we can use some generalized equations called the Projectile Kinematic Equations.
By using these equations we can find where that ball is going to land, depending on its initial velocity, mass, initial position, and time in the air.

Angle of release
We can find out the acceleration of the shot, and we can use the kinematic equations to tell us many things about the shot. But we don't know the optimal angle at which to release the ball. The typical optimal angle for a shot is between 45-55 degrees. This allows the shot to have a balanced height and speed on its way to the hoop (Blazevich 2007). A larger angle will give the shot more height and a smaller angle will give it a greater velocity and range. Both of these aspects are important, a ball that is shot with a larger height will have a larger target, but a ball with two much height won't have the speed and range its takes to reach the basket.