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OPTIMIZATION OF A BALL'S LAUNCH IN SPORTS

Abstract

Newton's law of motion is used to study the effects of air resistance on an object's motion. In ball-related sports such as baseball, soccer, etc., understanding the effects of air resistance is essential to optimize ball launch performance. This performance optimization can be studied by identifying the minimal time it takes for a ball with speed v to travel a certain distance. We work with two models that apply to an object's motion. In model 1, we make use of a linear air drag force, f=cv, where c, has units of kg/s. In model 2 we make use of a quadratic air drag force, f= γv^2, where γ has units of kg/m. Newton's second law leads to a differential equation, which can be solved to obtain the object's total air time. By differentiating this function, one can identify the minimum time of flight and thus optimize the launch efficiency. The analytic calculations are compared to MATLAB's numerical results.

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