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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

Analytic Approximations of Projectile Motion with Quadratic Air Resistance