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There is a solution presented in terms of the slope angle by A. Tan, C. H. Frick, and O. Castillo, “The fly ball trajectory: An older approach revisited,” American Journal of Physics, Vol. 55, pp. 37–40, 1987. But the slope angle is unknown except at the top (zero) of the trajectory, and can be found only numerically or graphically. Therefore, the solution is not in closed form.

has been cited by the following article:

• TITLE: Analytic Approximations of Projectile Motion with Quadratic Air Resistance

  AUTHORS: R. D. H. Warburton, J. Wang, J. Burgdörfer

  KEYWORDS: Projectile Motion, Air Resistance Quadratic

  JOURNAL NAME: Journal of Service Science and Management, Vol.3 No.1, March 29, 2010

  ABSTRACT: We study projectile motion with air resistance quadratic in speed. We consider three regimes of approximation: low-angle trajectory where the horizontal velocity, u, is assumed to be much larger than the vertical velocity w; high-angle trajectory where ; and split-angle trajectory where . Closed form solutions for the range in the first regime are obtained in terms of the Lambert W function. The approximation is simple and accurate for low angle ballistics problems when compared to measured data. In addition, we find a surprising behavior that the range in this approximation is symmetric about , although the trajectories are asymmetric. We also give simple and practical formulas for accurate evaluations of the Lambert W function.