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Introductory Physics Homework Help
How Does Rocket Ejection Mass Affect Its Velocity in Space?
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[QUOTE="Father_Ing, post: 6580201, member: 694574"] [B]Homework Statement:[/B] - [B]Relevant Equations:[/B] momentum conservation Consider a rocket with mass ##m## in space is going to move forward. In order to do so, it needs to eject mass backwards. Let the mass that is ejected has velocity ##u## relative to the rocket. What is the equation for the final velocity? It is said that after ##dt## second, the rocket will have mass ##m-dm##, and velocity ##v+dv##.But, isn't it also possible for the speed to increase in high sum after a very small amount of time, or even, not changing at all? And I tried to find this out by using conservation of momentum. Let ##v'## be the rocket's speed after ##dt## second, and ##v## is the initial speed. $$mv = dm(v-u)+(m-dm)v'$$ $$v'=\frac {(m-dm)v +udm}{m-dm}$$ $$v'=v+\frac {udm}{m-dm}$$ Since ##dm## is small, we can take the limit of dm->0. Therefore,$$v'= v$$ It can be concluded that the velocity neither increase nor decrease. But, I searched about this matter in the internet, and they said that ##v'## is ##v+dv##. Are there any mistakes in my method? [/QUOTE]
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How Does Rocket Ejection Mass Affect Its Velocity in Space?
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