Analytic Solution of Projectile Motion with Quadratic Drag and Unity Thrust

This paper introduces the analytic solution of a two-dimensional motion of a constant-mass projectile experiencing the resistant force parallel its velocity vector and constant gravitational force. The nonlinear governing equations describing the motion of the projectile are formulated in terms of the particle's speed and flight path angle and exact time-explicit/time-implicit solutions of the problem are derived. Numerical simulations were conducted to validate the correctness of the proposed solutions. In additions, the necessity of the solutions is explained with example applications.