How can you use mathematics to catch a baseball? The flight path of a baseball is a simple geometric shape called a parabola. It turns out that if you are standing in the flight path, then the slope of your line of sight to the baseball will increase at a constant rate. In order to catch a fly ball, an outfielder should position himself on the field so that the ball appears to be rising straight up at a constant speed.
The following GeoGebra worksheet demonstrates this concept. Point B controls the apparent horizontal distance from the outfielder to the ball, and Point A is the apparent position of the ball. The red line is a graph of the apparent height of the ball as a function of time. Notice that the ball appears to be rising at a constant rate from the outfielder's point of view. Press play or drag the red X to make things go.