Forest UCM Ch3 Rockets

Consider a rocket of mass [math]m[/math] moving at a speed [math]v[/math] ejecting rocket fuel for propulsion.

File:Forest UCM Ch3 Rockets Fig.xfig.txt

[math]m =[/math] mass of Fuel + Rocket

[math]-dm =[/math] mass of Fuel ejected over time interval [math]dt[/math] ( [math]dm[/math] = mass lost by rocket < 0)

[math]u =v_{FR}[/math] velocity of Fuel relative to the Rocket

[math]v =[/math] velocity of rocket relative to the ground before ejecting fuel of mass [math](-dm)[/math]

[math]v+dv =v_{RG}[/math] velocity of the rocket relative to the ground after ejecting fuel

[math]V_FG =[/math] Velocity of the fuel with respect to the ground

Conservation of Momentum

[math]mv = (-dm)V_{FG} + (m-(-dm))(v+dv)[/math]

[math]-dmV_{FG} = mdv + dm (v+dv)[/math]

The veocity of the fuel with respect to the ground may be written as the vector sum of the rocket velocith with respect to the ground and the velocity of the fuel with respect to the rocket (Galilean transormation)

[math]\vec{V}_{FG} - \vec{V}_{FR} + \vec{V}_{RG}[/math]

Forest_UCM_MnAM#Rockets