Highly precise analytic solutions for classic problem of projectile motion in the air

Abstract

Abstract Here is studied a classic problem of the motion of a projectile thrown at an angle to the horizon. The number of publications on this problem is very large. The air drag force is taken into account as the quadratic resistance law. An analytic approach is used for the investigation. Equations of the projectile motion are solved analytically. All the basic functional dependencies of the problem are described by elementary functions. There is no need to study the problem numerically. The found analytical solutions are highly accurate over a wide range of parameters. The motion of a baseball and a badminton shuttlecock is presented as examples.