Аннотация:The range maximization problem and corresponding the brachistochrone problem withCoulomb, viscous friction and accelerating force are considered. Normal component of the reactionforce and the thrust are considered as a control variables. A Maximum Principle procedure is appliedto reduce optimal problem to the boundary-value problem for the system of two nonlinear differentialequations. Solutions of this system are corresponding to the motion under singular control for normalcomponent of the reaction force and “bang-bang” control for the thrust. The qualitative analysis of thesolutions is carried out. It allows to install the characteristic properties of the trajectories, unnoticed in a number of publications as well as to confirm the hypothesis and the results of numerical calculations presented in other sources.