Numerical Solution of Free-Fall Equation Using Two Different Approaches of the Taylor Series Expansion

The idea of using the Taylor Series Expansion to solve non-differentiable equations arose from a student challenge in the numerical methods class. In order to convince the students that the numerical methods had substantial importance in solving equations encountered in engineering design, the students were challenged to find the velocity of free-falling object at a given time using 4th (or higher) order Taylor Series Expansion assuming that the original equation (both with linear and quadratic relation of air resistance with the velocity) could not be mathematically differentiated. Unfortunately, none of the students came up with a solution since there was no explicit solution was found over the internet. The case had led to sharing the idea and the example for the colleagues who might be willing to use them in their classes.