Some remarks on projectile motion with a linear resistance force

In this article we revisit the projectile motion assuming a retarding force proportional to the velocity, \(\vec{F_r} = -mk\vec{V}\). We obtain an analytical expression for the set of maxima of the trajectories, in Cartesian coordinates, without using the Lambert \(W\) function. Also, we investigate...

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Bibliographic Details
Published in:arXiv.org 2023-10
Main Authors: Morales, C A, Muñoz, J H, Vera, C E
Format: Article
Language:English
Subjects:
Cartesian coordinates
Classical mechanics
Kinetic energy
Mathematical analysis
Parameters
Potential energy
Projectiles
Online Access:Get full text
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Summary:In this article we revisit the projectile motion assuming a retarding force proportional to the velocity, \(\vec{F_r} = -mk\vec{V}\). We obtain an analytical expression for the set of maxima of the trajectories, in Cartesian coordinates, without using the Lambert \(W\) function. Also, we investigate the effect of the parameter \(k\) on the radial distance of the projectile showing that the radial distance oscillates from a certain critical launch angle and find an approximate expression for it. In our analysis, we consider the impact of the parameter \(k\) in the kinetic energy, the potential energy, the total energy and the rate of energy loss, and in the phase space. Our results can be included in an intermediate-level classical mechanics course.
ISSN:2331-8422
DOI:10.48550/arxiv.2310.01776