An Optimal Angle of Launching a Point Mass in a Medium with Quadratic Drag Force

Abstract

A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. Analytic approach is used for investigation. The problem of finding an optimal angle of launching a point mass in a medium with quadratic drag force is considered. An equation for determining a value of this angle is obtained. After finding the optimal angle of launching, eight main parameters of the point mass motion are analytically determined. These parameters are used to construct analytically six main functional relationships of the problem. Simple analytic formulas are used to solve two problems of optimization aimed to maximize the flight range of a point mass and minimize the initial speed of the point mass for getting to the given point on the plane. The motion of a baseball is presented as an example.