# The Physics of Shooting

Information revealed by Dr. John Fontanella in his book The Physics of Basketball shows that launch speed is determined by the amount of force you apply to get the ball to the goal.  How much force is necessary is determined by your distance from the goal.  For example, when shooting a 2-foot shot, you only need a launch speed of approximately 10 miles per hour.  For a 3-point shot you need a launch speed of approximately 18 miles per hour.  More force (speed) is necessary for longer shots to get the ball to the basket.

Launch angle is simply the angle at which you launch the basketball towards the basket.  For our discussion here, having your arm straight out and parallel to the floor is a 0-degree angle.  Having your arm straight up pointing to the ceiling is a 90-degree angle.  Halfway in-between these two extremes would be a 45-degree angle.  Your distance from the goal and the release height of your shot determine the ideal launch angle for a slow moving ball at the rim.  The closer you are to the basket, the higher your launch angle will be.  A two-foot shot released from a height of 8-feet, requires a launch angle of 72 degrees to produce the slowest moving ball at the rim.  As you move away from the basket, your launch angle decreases, a free throw is approximately 51 degrees and a 3-point shot is approximately 45-degrees.

The release height of the basketball shot is largely determined by the height of the player shooting.  According to Professor John Fontanella, the ideal angles from the free throw line are as follows:

• 5’4″ player should launch the ball at a 52.2 degree angle
• 5’8″ player should launch the ball at a 51.5 degree angle
• 6’0″ player should launch the ball at a 50.8 degree angle
• 6’4″ player should launch the ball at a 50.1 degree angle
• 6’8″ player should launch the ball at a 49.4 degree angle
• 7’0″ player should launch the ball at a 48.7 degree angle

These angles produce the slowest moving ball as it approaches the rim, which gives you a shooter’s touch.

HIGHER ARC = BIGGER TARGET

Shooting is an optimization process.  Complicating this matter is the fact that your target area increases with a higher launch angle.  The higher the arc, the larger the target.  In theory it makes sense to shoot with an exaggerated high arc, thereby increasing the size of your target.  However, higher arc requires more force at the time of release to propel the basketball higher, which makes it more difficult to control the shot.  In addition, the shot will no longer be a ‘soft shot’ because gravity increases the speed of the ball as it falls.  For each 0.1 second the basketball falls through the air, it increases in speed.  The faster the ball is moving, the greater the collision with the rim.

Conversely, with a low arc you also need to utilize more force to get the basketball to the rim.  A low launch angle requires more initial speed upon release to get the ball to the basket.