Some remarks on projectile motion with a linear resistance force

Abstract

Abstract In this article, we revisit projectile motion assuming a retarding force proportional to the velocity, F r ⃗ = − mk 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 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 parameter k in the kinetic energy, the potential energy, the total energy, the rate of energy loss, and the phase space. Our results can be included in an intermediate-level classical mechanics course.