Calculate Speed of Exhaust Gas in Rocket Propulsion

[justin016]

Homework Statement

A Rocket is propelled as a result of the very rapid ejection of exhaust gas from the rear of the rocket. Given that the initial mass of the rocket and fuel is 5000kg and the 4000kg of fuel is burned in accelerating the rocket to a speed of 600m/s, calculate the speed of the exhaust gas

Homework Equations

(M+delta(m))v = M(v+delta(v)) + delta(m)(v-ve)

M=mass of the rocket
delta(m)= mass of the fuel
v= velocity of the system
v+delta(v)= velocity of the rocket after ejection
ve= velocity of the exhaust

The Attempt at a Solution

equating the above equation given me ve= (M*delta(v))/(delta(m))=
(1000)(600)/4000 = 150m/s


I have a feeling this not quite that simple, and the solution is completely wrong.
1. is the exhaust speed is the speed of the fuel after or before the ejection?

 

[XanziBar]

I think you can derive the rocket equation using conservation of momentum.
http://en.wikipedia.org/wiki/Tsiolkovsky_rocket_equation