Help with final velocity of a rocket

AI Thread Summary
To calculate the final velocity of a rocket with an initial mass M0 and final mass Mr, while ejecting gas at velocity c, the conservation of momentum principle is applied. The total momentum of the system, which includes the rocket and the ejected gas, must remain zero. The equation M0*v - (M0-m)*c=0 is established, but the final velocity of the gas is not constant as it depends on the rocket's velocity. A differential equation is suggested to account for the changing mass of the rocket as gas is ejected. Further assistance is requested to clarify the momentum conservation equation as the mass transitions from m to m - dm.
PhysicsLoop
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Homework Statement


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.


Homework Equations


We have to calculate the final velocity of rocket.


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?
 
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Welcome to PF!

Hi PhysicsLoop! Welcome to PF! :smile:
PhysicsLoop said:
Because the total momentum of an isolated system is conserved, the total system - rocket + exhausted gas - must still have zero momentum.

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. :wink:
 
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.
 
v is a function of m

write the equation for conservation of momentum when the mass changes from m to m - dm
 
I still don't get it... Can you write it please?
 
Can someone help me with this?
 

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