Masters Theses

Date of Award

8-1999

Degree Type

Thesis

Degree Name

Master of Science

Major

Mathematics

Major Professor

Steven Serbin

Abstract

The branch of mathematical analysis that involves the determination of trajectories (flight paths) of projectiles is known as ballistics. Historically, ballistics has been applied to designing weapons of war. The shape of the trajectory of a projectile is uniquely determined by the velocity and angle at which it is launched. In this thesis, ballistics is applied to determine if the trajectory of a basketball shot from a particular location, relative to the rim, will be successful, i.e., will pass through the rim. The determination of whether a basketball shot launched from a particular . location is successful depends on relationships between the shape of the trajectory and geometrical constraints imposed by the spherical shape of the ball and the circular shape of the rim.

A computational methodology is developed to generate the solution of all trajectories for which a basketball released from the hand of the shooter at a particular location would be successful. Numerical results are presented that illustrate the application of this computational methodology for a sampling of cases. These include the case where gravity is the only force acting on the projectile and also the case where the drag force due to air resistance is included in the formulation.

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