Homework Help: Help with final velocity of a rocket

1. Oct 24, 2012

PhysicsLoop

1. The problem statement, all variables and given/known data
Calculate the final velocity of a rocket if the velocity of the ejected gas is c, initial mass of rocket is M0 and final mass is Mr, v0=0.

2. Relevant equations
We have to calculate the final velocity of rocket.

3. The attempt at a solution
Because the total momentum of an isolated system is conserved, the total system - rocket + exhausted gas - must still have zero momentum.
If the velocity of gas is c, then:
M0*v - (M0-m)*c=0
m - mass of gas ejected

What to do next?

2. Oct 24, 2012

tiny-tim

Welcome to PF!

Hi PhysicsLoop! Welcome to PF!
Ah, but you don't know what the final velocity of the gas is (it changes according to the velocity of the rocket at the time).

You'll need to write a differential equation for what happens when the speed is v and the mass is m, and a small amount of mass dm is ejected.

3. Oct 24, 2012

PhysicsLoop

Thanks! :)
Velocity of the gas is constant equal with c (speed light), it doesn't change with rocket velocity.
Can you help me? I'm stucked.

4. Oct 24, 2012

tiny-tim

v is a function of m

write the equation for conservation of momentum when the mass changes from m to m - dm

5. Oct 24, 2012

PhysicsLoop

I still don't get it... Can you write it please?

6. Oct 25, 2012

PhysicsLoop

Can someone help me with this?