The Physics of the Basketball Shot
Newtons 3rd Law
As we learned back in Physics 211 we understand fully that Newton's 3rd law states that with every reaction, there is an equal and opposite reaction. The same is applied to the physics behind the basketball shot. As you can see in figure 1 to the right, you can see just how Newton's 3rd law works. As you shoot, this applies a force, F=ma, and after it is released it will do an equal and opposite force in the opposite direction. Along with this velocity the ball is encountering, it also will experience spin from the friction of your hands.
To get an understanding of the basketball we need to look at the velocity that is needed to achieve the main objective of basketball, to get the basketball into the hoop. If you are 2 feet away from the goal, this will take about 10 miles per hour (mph) of speed for the ball to reach the correct distance and height of the basketball goal. For a 3-point shot, it will take roughly 18 mph of sped to reach the correct distance and height of the goal at 10 feet in height. Of course, as you get further out, which most NBA players will shoot from, you will need to apply more force, creating more speed, in order to reach the basketball goal.
This is the angle at which you intend to release the basketball as you shoot the ball towards the goal. This is measured between the x-axis and z-axis, where x is 0 degrees and since we are in 3-D the z-axis will be at 90 degrees. if you are two feet away form the basketball goal, and if release the ball from roughly 8 feet above the basketball court, you will need to release it at roughly 72 degrees to create the best shot. If you are shooting a 3 pointer, this requires a shot between 45 and 48 degrees. The free throw, which is shot because of a foul, is the fundamental place to get easy points. At this location, it is better to release the basketball around roughly 51 degrees. With this launch angle, this creates a better arc, path in the air, in other words, a higher arc, will potentially create a bigger target when the ball reaches the goal.
Figure 1 above shows Newtons 3rd law applied in a basketball shot.
Figure 2 above shows the Physics of the ideal, and best 3-point shot in the NBA.