Some problems of the projectile motion with a square-law resistance

TL;DR

This paper investigates how quadratic resistance affects projectile motion characteristics, providing numerical and analytical methods to optimize flight range and trajectory length, with practical examples like baseball and shuttlecock motion.

Contribution

It introduces methods to analyze and optimize projectile motion with quadratic resistance, including numerical and analytical approaches, which are applied to real-world sports objects.

Findings

Maximized flight range and trajectory length under quadratic resistance

Constructed loci for optimal projectile characteristics

Analyzed motion of sports objects like baseball and shuttlecock

Abstract

The influence of the force of the quadratic resistance of the medium on the change in some interesting characteristics of the motion of the projectile, which take place when the projectile moves in vacuum, is investigated. Loci that ensure maximization of the flight range, the arc length of the projectile trajectory and a non-decreasing of the length of the radius-vector are constructed numerically (and partly analytically). As examples, the motion of a baseball, a tennis ball and a badminton shuttlecock is studied.