Newton's laws are 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 to travel a certain distance. We work with two models that apply to an object's motion. One of the models assumes a linear air drag while a second model makes use of a quadratic air drag. We do investigate known differential equations for when the Magnus force is present as well as absent. This is done through numerical and analytic solutions, when possible. The development of approximations leads to differential equations that are suitable for time optimization studies The analytic calculations are compared to MATLAB's numerical results. We concentrate on situations for which the speed of the projectile parallel to the ground is much greater than its speed perpendicular to it.


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