In the field of physics and in particular that of ballistics, a problem has been attributed to Sir Isaac Newton. He, supposedly, proposed a problem, some 350 years ago, to provide a closed form solution to the trajectories of objects either tossed or fired into the air considering the resistance of the atmosphere. This is a classic problem taught in all high school and college physics courses. However, the problem has been over simplified in order to obtain a solution. The equations of motion have never been solved when atmospheric drag has been properly taken into account. 
 
While the equations of motion still have not been successfully integrated with respect to time, the author has made some valuable progress toward a solution by integrating the equations with respect to the flight path angle. The equations are shown to be solvable in this manner. However, some solutions necessarily had to be left as unevaluated integrals. Special case scenarios are also shown with their closed form solutions. Finally, the paper provides ideas and recommendations for future research.

Advancements In Solving Ballistic Equations Involving Quadratic Drag PDF

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