The motion of a solid particle introduced into a stream of fluid is a crucial problem in the contexts of pneumatic transport and the purification and separation of non-uniform mixtures. However, the complexity of the underlying equations of motion enforces the creation of semi-empirical models. Therefore, analysis of particle motion in a pneumatic channel was performed. To reduce the number of independent variables, several simplifying assumptions were made in regard to both the particle and the stream. The resulting model provides trajectory equations for a particle introduced into the stream at given values of the initial angle and initial velocity, which are then solved using numerical integration methods. A hodograph function was formulated on the basis of the Runge−Kutta and NDFs methods to test the correctness of the solutions under various initial parameters and to provide a universal method of solving the equations of motion. To verify the model, terminal velocities were measured and particle trajectories recorded using an original experimental stand. The predictions of the model were subsequently compared to these empirical trajectories and were found to fall within the range of uncertainty.