Abstract
Here is studied a classic problem of the motion of a projectile thrown at an angle to the horizon. 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 for 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 are presented as examples.
Highlights
The problem of the motion of a projectile thrown at an angle to the horizon in midair has a long history
In the given paper an analytic approach is used for the investigation of the projectile motion in a medium with quadratic resistance
The proposed analytical solution differs from other solutions by simplicity of formulae, ease of use and high accuracy
Summary
The problem of the motion of a projectile thrown at an angle to the horizon in midair has a long history. The proposed formulas make it possible to study the motion of a projectile in a medium with the resistance in the way it is done for the case without drag. These formulae are available even for first-year undergraduates. Many approximate solutions use special functions, for example, the Lambert W function This is why the description of the projectile motion by means of a simple approximate analytical formulae under the quadratic air resistance is of great methodological and educational importance. The purpose of the present work is to give a simple formulas for the construction of the trajectory of the projectile motion with quadratic air resistance. The conditions of applicability of the quadratic resistance law are deemed to be fulfilled, i.e. Reynolds number Re lies within 1×103 < Re < 2×105
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