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.
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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Ballistic shooting at constant acceleration