Range and flight time of quadratic resisted projectile motion using the Lambert <i>W</i> function

Abstract

We study projectile motion with air resistance quadratic in speed. An approximation of a low-angle trajectory is considered where the horizontal velocity, vx , is assumed to be much larger than the vertical velocity, vy . The explicit solutions for the range and flight time are expressed in terms of the secondary branch of the Lambert function, . In addition to their theoretical importance, the results obtained will be of interest to teachers involved in undergraduate physics courses.