On the locus formed by the maximum heights of projectile motion with air resistance

We present an analysis on the locus formed by the set of maxima of the trajectories of a projectile launched in a medium with linear drag. Such a place, the locus of apexes, is written in terms of the Lambert "W" function in polar coordinates, confirming the special role played by this fun...

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Bibliographic Details
Published in:European journal of physics 2010-11, Vol.31 (6), p.1319-1329
Main Author: Hernández-Saldaña, H
Format: Article
Language:English
Subjects:
College Science
Communication, education, history, and philosophy
Equations (Mathematics)
Exact sciences and technology
General physics
Motion
Physics
Physics literature and publications
Science Experiments
Scientific Principles
Surveys and tutorial papers, resource letters
Undergraduate Students
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Summary:We present an analysis on the locus formed by the set of maxima of the trajectories of a projectile launched in a medium with linear drag. Such a place, the locus of apexes, is written in terms of the Lambert "W" function in polar coordinates, confirming the special role played by this function in the problem. To characterize the locus, a study of its curvature is presented in two parameterizations, in terms of the launch and the polar angles. The angles of maximum curvature are compared with other important angles in the projectile problem. As an addendum, we find that the synchronous curve in this problem is a circle as in the drag-free case. The presentation is suitable for advanced undergraduate students. (Contains 6 figures and 2 footnotes.)
ISSN:0143-0807
1361-6404
DOI:10.1088/0143-0807/31/6/002