The subject of the research is a model of a magnetic launcher, which is an innovative alternative to commercially occurring unmanned aircraft launchers (UAV). As the take-off is an energy-demanding phase of the flight; therefore, abandoning the power supply of the UAV during this phase significantly affects increasing the potential range and duration of UAV flight. The magnetic launcher offers the significant advantage of minimizing friction between the starting cart and the launcher, resulting in the higher energy efficiency of the system. Research conducted so far has shown that the possibility of accelerating the aircraft on the longer runway offered by the launcher reduces aircraft overloads occurring during take-off. As a result, the launcher, aircraft, and onboard equipment are much safer. This paper presents the system’s mathematical modeling and numerical simulation results for micro-class UAV take-off and landing using the analyzed magnetic launcher. The computer program for analyzing system dynamics was implemented in the MATLAB environment. Simulation results were visualized graphically and as animations in Virtual Reality. The VR application was implemented in Unity and ran on VR goggles Oculus Quest2. The simulations carried out show that—in the absence of control—an important factor reducing the takeoff distance and affecting the aircraft load is the adoption of a non-zero takeoff thrust of the UAV. The initial pitch angle also has a significant impact on the takeoff process. With an increase in this parameter, the length of the takeoff distance decreases and the lift-off speed decreases, but too much pitch angle may result in the aircraft descending in the first moments of flight, which could lead to a collision with the launch rails.