Mathematics in Sports


We’ve all heard the joke of the smart kid playing a game of basketball and how he calculates the angle and speed the ball goes to land inside the hoop. While it may sound daunting, there are very simple physics formulas that can determine multiple plays in sports such as the range a ball needs to travel in baseball, the momentum of a football player to break a tackle, or even the force of impact a ball can make when hitting a football player. So how can we calculate some of these plays performed by superstar athletes?


Let’s take basketball star Stephen Curry for example, as seen in the YouTube video:

Curry shoots the ball from beyond the three-point line at an approximate 45-degree angle (the angle that is most ideal for a basketball shot). What we can do is take the formula for the range of the hoop. After, we can take the equation:

*Sine is equal to the ratio between a right triangle’s opposite side and its hypotenuse.

* Theta is equal to the angle at which the ball is being shot at.

After Rearranging the equation, we can determine that the exact speed the ball needs to be thrown at to make it inside the hoop is approximately 34.2 feet per second! With this in mind, using the range of the actual three-point line (25 feet), we can determine that a speed of 28.3 feet per second is needed to ideally sink a three point shot!

Next we’ll take a look at the amount of force it takes superstar athlete J.J. Watt to tackle Alex Smith.

After examining the video, it is determined that it takes JJ Watt 4 seconds running at a speed of 7.5 feet per second to reach Alex Smith. So using Newton’s original Second Law of Motion:

it can be determined that Watt delivers a stunning 541 Pounds of Force or 2406 Newtons!

Finally, let’s have a look at the amount of kinetic energy generated by world famous sprinter Usain Bolt. Usain Bolt, the fastest man in the world, has been known to hit terminal speeds of 12.4 meters per second (28 miles per hour). Using the Kinetic Energy Formula, we can determine how much energy Usain Bolt generates simply hitting his terminal speed.

After analyzing the video, the equation for kinetic energy was used to calculate how much energy would be generated after his sprint. (Assuming friction is negligible)

We can determine that Usain Bolt Generates a whopping 16,067 Joules of Energy or 1514 Watts, which is approximately equal to 2.00 Horse Power!


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