Answer:
The vertical trajectory is governed by Ordinary Differential Equation.
Time derivatives of each state variables.
d(d)/dt = v, d(m)/dt = -d(m-fuel)/dt, d(v)/dt = F/m.
Where V is velocity positive upwards, t is time, m is mass, m-fuel is fuel mass, F is Total force, positive upwards.
Therefore,
F = -mg - D + T, If V is positive and
F = -mg + D - T, If T is negative.
D is drag and the questions gave it as zero.
Explanation:
The two sign cases in derivative equations above are required because F is defined positive up, so the drag D and thrust T can subtract or add to F depending in the sign of V . In contrast, the gravity force contribution mg is always negative. In general, F will be some function of time, and may also depend on the characteristics of the particular rocket. For example, the T component of F will become zero after all the fuel is expended, after which point the rocket will be ballistic, with only the gravity force and the aerodynamic drag force being p
