Help with final velocity of a rocket

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Homework Help Overview

The discussion revolves around calculating the final velocity of a rocket based on the conservation of momentum, given the velocity of the ejected gas and the initial and final masses of the rocket.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the conservation of momentum in the context of the rocket and ejected gas, with one participant attempting to set up an equation based on momentum conservation. Others question the assumption of constant gas velocity and suggest the need for a differential equation to account for changing mass.

Discussion Status

There is an ongoing exploration of the problem, with participants offering insights and questioning assumptions about the gas velocity and the relationship between the rocket's mass and velocity. Some guidance has been provided regarding the need for a differential approach, but no consensus has been reached.

Contextual Notes

Participants are grappling with the implications of the gas velocity being constant and how that affects the momentum conservation equation. There is also a mention of the need to consider changes in mass during the rocket's flight.

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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