Abstract
<title>Abstract</title> <p>The basketball free throw is a prime example of projectile motion in which the trajectory is affected by gravity and aerodynamic forces. While ideal projectile motion cases neglect air resistance, its pressence in the real world can effect the free throw in ways we can’t see. This study explores how linear air resistance affects the optimal launch angle of an NBA free throw. Two mathematical models - one with and one without air resistance - were developed using Newton’s second law and the resulting differential equations were resolved analytically using numerical optimization using Python. As such, this study concluded that in a standard NBA arena, the optimal launch angle neglecting drag is 51.4° and 49° when linear air resistance was inlcuded. Conclusively, the study displays how linear air resistance introduced a decrease in the optimal launch angle of the free throw by 2.4°. Further trajectory comparisons showed how air resistance lowered the apex of the shot and decreased the range of the shot.</p>