Horizontal distance traveled by a mobile experiencing a quadratic drag force: normalized distance and parametrization

Alexandre Vial - alexandre.vial_AT_utt.fr
Pôle Physique, Matériaux et Nanotechnologies
Université de technologie de Troyes
12, rue Marie Curie BP-2060 F-10010 TROYES Cedex

Published in Eur. J. Phys. 28(4), July 2007

Abstract

We investigate the problem of the horizontal distance traveled by a mobile experiencing a quadratic drag force. We show that by introducing a normalized distance, the problem can be greatly simplified. In order to parametrize this distance, we use the Pearson VII function, and we find that the optimal launch angle as a function of the initial velocity can also be fitted by this function.

1 Introduction
2 Numerical study
 2.1 Normalized distance
 2.2 Parametrization
 2.3 Example of application
3 Conclusion
A Limit of the Pearson function for M →∞
References