Many attempts have been made at finding the trajectory for the projectile problem with quadratic drag. However, no complete analytical solution is possible due to the nonlinear coupling between differential equations describing the horizontal (x) and vertical (y) velocity components that result in the final trajectory solution, y = f(x). Over the years, a number of approximate analytical methods, including Taylor series expansions, have been applied to the problem. However, whereas prior works expanded Vx by assuming Vx = Vx(t), the expansion here is based on the faster converging 1/Vx(t), whose reciprocal better captures the monotonically decreasing nature of Vx.
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