Sports Mathematics

Let's look at the throwing and hitting of a baseball.  The pitcher wants to throw the ball so that he will strike out the batter.  If his throw is too high or low then it is a ball and the better still has at least three more opportunities to hit the ball.  Similarly, when the batter hits the ball, he wants to hit the ball so that it will be as far away from any of the other players as possible if not outside of the ball field itself.  The players must take into consideration the speed and height of the ball to ensure that they will throw or hit it properly.  Here is the equation for finding the projectile motion of a baseball will travel:

where all distances are measured in feet, ho is the height from which the ball is thrown, α is the angle at which the ball is thrown, vo is the speed at which the ball is thrown, and x is the distance that the ball travels.  We can find the distance that the ball will travel by saying

Now, a batter would be more concerned with the range of the ball, wanting it to travel far enough to allow him to at least make it to first base safely.  Let's look at several graphs of the range with different α's and a fixed vo and ho.

Simply not enough space to show the entire equation, but it offer's fans the opportunity to see we're not simply playing games on the field.