Basketball players score with physics

     Who knew that professional and collegiate basketball players are instinctual physicists? Many physics professors agree that it is not easy to shoot a three-pointer – there are many factors that come into play on the court in order to make that perfect shot.

A three-point field goal, which is also known as a "three-pointer,” is a field goal in a basketball game that is made from beyond the three-point line, a designated arc radiating from the basket. A two-point field goal, in contrast, is made inside the three-point line. A three-pointer is one of the hardest shots to make in a game.

What makes it so hard? According to Creighton University physics professor Gintaras Duda, Ph. D., basketball players have to consider many different factors on the spot before they take the shot, including launch speed, launch angle, release height, and high and low arcs.

Launch speed is determined by the amount of force you apply to get the ball to the goal which, in turn, is determined by your distance from the goal.  For example, when shooting a two-foot shot, you only need a launch speed of approximately 10 miles per hour.  For a three-point shot you need a launch speed of approximately 18 miles per hour.  Basic physics dictates that more force is necessary for longer shots to get the ball to the basket.

Launch angle is the angle at which you shoot the ball towards the basket.  For our discussion here, sticking out your arm so that it is parallel to the floor is a 0° angle.  Having your arm straight up pointing to the ceiling is a 90° 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 have to be. A two-foot shot released from a height of eight feet requires a launch angle of 72° to produce the slowest moving ball at the rim.  As you move away from the basket, your launch angle decreases.

Complicated, right? But that’s not all.

It turns out that there are even more forces that act upon the ball once it leaves the player’s hands. The author of the book The Physics of Basketball, John Fantanella, explains that many basketball players give the ball a little bit of backspin, which allows the ball to travel through the air at the lowest possible speed, which in turn gives the ball a bit of lift. This is known as the Magnus effect, and many players use this technique so that if the ball hits the backboard or rim, there will be a less violent rebound and a higher chance for the ball to go through the hoop.

Making a three-pointer requires a perfect blend of all of these elements. From his research, Duda concluded that the lowest arc required for even a hope of making a three point shot is 33 degrees. Ideally for a perfect three-pointer, a player should stand exactly 20.9 feet away from the basket and aim for an arc of 45 degrees, a speed of just under 20 miles per hour and two revolutions per second of spin. But on the court in the heat of the moment, it is a lot to think about – not everyone can be physicists, so consistency in shooting three-pointers all boils down to repetition and practice.

Zac Zilber, a freshman who plays in the Hopkins intramural basketball league, agrees that shooting a three-pointer is all about instinct. In an interview Zilber stated, “In the end, it’s all about muscle memory and practicing.”