On the problem of projectile motion in a medium with quadratic resistance

TL;DR

This paper presents an accurate approximate analytical solution for projectile motion in a medium with quadratic resistance, applicable across various initial conditions and demonstrated with multiple real-world examples.

Contribution

It introduces a universal formula for projectile motion with quadratic resistance, valid for diverse initial conditions and medium resistance coefficients.

Findings

High-accuracy approximate solutions derived

Formulas applicable to various initial conditions

Validated with examples like shuttlecock and bullets

Abstract

A classic problem of the motion of a projectile thrown at an angle to the horizon in a medium with a quadratic resistance law is studied. An approximate analytical solution of the equations of projectile motion is presented, which has a high accuracy. The proposed formulas are universal, that is, they can be used for any initial conditions of throwing over a wide range of the change of medium resistance coefficient. The motion of a shuttlecock of badminton, bullet, table tennis ball and volleyball are presented as examples.