Question

A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times the mass of the empty rocket. Part A What is the rocket's speed when half the fuel has been burned?

Answer 1

Answer:

 $v_{f}$ = 1,386 m / s

Explanation:

Rocket propulsion is a moment process that described by the expression

       $v_{f}$ - v₀ =  $v_{r}$ 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

       $v_{f}$ - 0 = 2000 ln (5Mf / 2.5 Mf) = 2000 ln 2

       $v_{f}$ = 1,386 m / s