The simulation allows the user to adjust the initial speed and launch angle of the projectile using sliders. The projectile is launched from the top of the mountain (note that the mountain shown in the diagram is ridiculously tall - such a mountain would stick out above Earth's entire atmosphere). The motion of the projectile is calculated using Newton's Second Law of motion and Newton's Universal Law of Gravitation.
The user has the option to allow the projectile to pass through Earth. The Earth is treated either as a homogeneous sphere (the default) or as a point mass located at its center (if selected in the Model Options menu). The homogeneous sphere is more realistic, but using the point mass can help illustrate the "true" shape of the projectile's path before it hits Earth.