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arXiv · 2310.01776

Some remarks on projectile motion with a linear resistance force

C. A. Morales·J. H. Muñoz·C. E. Vera
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Abstract

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.

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C. A. Morales, J. H. Muñoz, C. E. Vera. 2023-10-03. Some remarks on projectile motion with a linear resistance force. https://doi.org/10.1088/1361-6404/acf0a5

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