A flying baseball in the air not only is subject to gravity's pull it is also subject to air resistance. A spinning ball in addition to these two forces experiences a spin-dependent force. The description of motion of a baseball subject to these three forces for a projectile confined to trajectories in a 2D vertical plane is a set of two coupled nonlinear ODEs. The speed dependent drag coefficient makes these equations highly nonlinear. These equations for certain cases are solved numerically by applying a 4rth-order Runge-Kutta code written in either the FORTRAN or the C++ languages. In this article we show by deploying Mathematica one may easily bypass the explicit need of composing such cumbersome computer codes. Moreover, by utilizing Mathematica's integrated numeric and graphic features the author reveals features of a flying ball that to-date have not been reported in scientific literature.