An Analytical Solution for the Motion of a Projectile Accounting for Drag in the Case of Vertical Launch

Wadsworth, Fabian B. ; Llewellin, Edward W. und Vasseur, Jérémie (2024): An Analytical Solution for the Motion of a Projectile Accounting for Drag in the Case of Vertical Launch. In: Physics Teacher, Vol. 62, No. 6: pp. 497-500

Abstract

We study the problem of projectile motion, subject to atmospheric drag, in the special case of a vertical launch (i.e., straight up). We find that there exists an analytical solution for the time evolution of the projectile position and for the maximum height it will reach, when we assume that the drag coefficient has a constant value. We compare our solution with a full numerical solution in which the drag coefficient is allowed to vary nonlinearly as the projectile changes velocity. We suggest that the analytical solution we present provides a useful pedagogical bridge between full solutions to projectile motion problems, which typically require numerical methods, and the very simplest solutions, which can be inaccurate in many real-world applications.

• Item Type: Journal article
• EU Funded Grant Agreement Number: 834225
• EU Projects: Horizon 2020 > ERC Grants > ERC Advanced Grant
• Form of publication: Publisher's Version
• Faculties: Geosciences > Department of Earth and Environmental Sciences; Geosciences > Department of Earth and Environmental Sciences > Mineralogy, Petrology and Geochemistry
• Subjects: 500 Science > 530 Physics
• ISSN: 0031-921X
• Language: English