Flight mechanics is the application of Newton's laws to the study of vehicle trajectories (performance), stability, and aerodynamic control. This text is concerned with the derivation of analytical solutions of airplane flight mechanics problems associated with flight in a vertical plane. It presents algorithms for calculating lift, drag, pitching moment, and stability derivatives. Once an analytical solution has been obtained, numbers are calculated in order to compare the answer with the assumptions used to derive it and to acquaint readers with the sizes of the numbers. A subsonic business jet is used for these calculations.