Answer:
[tex]v_{f}[/tex] = 1,386 m / s
Explanation:
Rocket propulsion is a moment process that described by the expression
[tex]v_{f}[/tex] - v₀ = [tex]v_{r}[/tex] ln (M₀ / Mf)
Where v are the velocities, final, initial and relative and M the masses
The data they give are the relative velocity (see = 2000 m / s) and the initial mass the mass of the loaded rocket (M₀ = 5Mf)
We consider that the rocket starts from rest (v₀ = 0)
At the time of burning half of the fuel the mass ratio is that the current mass is
M = 2.5 Mf
[tex]v_{f}[/tex] - 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2
[tex]v_{f}[/tex] = 1,386 m / s
