1. Ballistic shooting at constant acceleration
The first problem dealt with is that of a ballistic launch on a flat Earth with no atmosphere. The aim is to maximize the range of a rocket fired from the ground at constant acceleration. This is a theoretical model, as the acceleration of a real rocket is decreasing due to mass loss. This model can be used as a first approximation, considering, for example, the average acceleration of the rocket during its flight.
1.1 Modeling
The trajectory is in the vertical plane (Oxz) shown in figure 1 . The Earth is assumed to be flat, with no atmosphere, and gravity is constant along the vertical (Oz).
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