Study of the projectile motion in the air using simple analytical formulas

TL;DR

This paper presents simple analytical formulas for projectile motion with air resistance, enabling easy calculation of trajectories and characteristics for various initial conditions without numerical methods.

Contribution

It introduces universal, accurate formulas for projectile motion considering quadratic air resistance, simplifying analysis for different objects and initial conditions.

Findings

Formulas accurately predict projectile trajectories with air resistance.

Applicable to various objects like baseballs, tennis balls, and shuttlecocks.

Eliminates need for numerical simulations in projectile analysis.

Abstract

A classic problem of the motion of a projectile thrown at an angle to the horizon is studied. Air resistance force is taken into account with the use of the quadratic resistance law. The projectile motion is described analytically with fairly simple formulas. They make it possible to calculate basic motion characteristics and trajectory as easily as in the case of a parabolic motion. There is no need to study the problem numerically. The proposed formulas are universal, that is, they can be used for any initial conditions of throwing. In addition, they have acceptable accuracy over a wide range change of parameters. The motion of a baseball, a tennis ball and shuttlecock of badminton are presented as examples.