# Slam dunk!

#### Forces & MotionRecreationSportsKinematicsDynamicsCircular MotionMathematicsMeasurement

Good basketball players can improve their game and improve their scoring by understanding some simple physics.

Did you know? The rim of the basket and the basketball have diameters of 18" and 9.5".

Players like Vince Carter or Michael Jordan know instinctively what to do during a game because of thousands of hours of playing and practice that have “hard wired” their brains to carry out the correct sequence of muscle movements. However, even though actions such as passing, cutting and shooting have been well practiced and can be readily repeated by a player, it doesn’t mean they are as good as they can be. This is where an understanding of simple physics and more particularly the science of mechanics can help.

Let’s look at a few examples.

Did you know? The hang time for a jump of 3 feet is constant at 0.87 seconds, no matter what you think you see.

When shooting a basketball, the player uses enough force to hopefully have the ball reach the net for a score. In the process, the shooter’s fingers are spread across the ball and usually along the seams. As the hand is pushed through the ball and wrist is flipped the fingers cause the ball to spin backwards. When the ball hits the rim or the back board, that back spin causes a change in the speed of the ball and gives it a greater chance of falling through the basket for a score. With reverse layups, top spin is used to make the ball speed forward and appear to jump into the basket!

Did you know? For jump shots with launch angles of 55 degrees and 45 degrees, the margin of error at the rim is 5” and 3”, respectively.

Shooting a jump shot requires a number of factors to be considered which include the height of the player, the force imparted to the ball or the speed at which it leaves the player’s hand (launch speed) and the launch angle of the ball. Since the ball travels in an arc, a greater launch angle increases the target area since the ball in approaching the rim on a more vertical path. However, the price to be paid for more arc is the use of more force or greater launch speed to get the ball to the net. This in turn makes the ball fall from a greater height and hit the rim or backboard with greater force reducing the chances of scoring. Good players by experience optimize their own launch angles instinctively and make the trade off between larger target area and shot softness in order to maximize scoring.

You can try this out yourself by running a jump shot simulation at the following web site: http://www.fearofphysics.com/Proj/proj.html

So remember, players' use high arcing shots to enlarge the target area and increase their scoring chances.

Science of the Slam

Article first published on November 11, 2009.

Photo Credit: Wikimedia Commons (originally posted to Flickr by Nathan Dainty)

#### Ken Dymock

I have an Honours B.Sc. in Chemistry and Mathematics from the University of Waterloo and a Ph.D. in inorganic chemistry from the University of Florida. I have done research and development work in the chemical, petroleum and mining industries and hold a number of patents.  My research interests have ranged from coordination chemistry and x-ray crystallography to metal purification, synthetic fuels, chemical and petroleum processing and fuels, chemical and lubricant product development.  In my spare time I like to garden and attempt to understand the physics of hitting a golf ball.