How Do You Derive the Tsiolkovsky Rocket Equation?

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The discussion centers on deriving the Tsiolkovsky rocket equation, starting with a rocket's mass, including fuel, and the ejection velocity of combustion products. A participant expresses difficulty in approaching the problem due to a lack of physics background and notes that the relevant formula was not provided in their differential equations textbook. They attempted to find the Tsiolkovsky formula online but encountered challenges. Helpful resources, including Wikipedia, are suggested for further reading. The conversation emphasizes the importance of understanding the underlying physics to successfully derive the equation.
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Homework Statement


The mass of a rocket, including a full chamber of fuel, is M. Its net mass without fuel is m. The products of combustion are ejected with velocity c. If the rocket starts from rest, derive Ciolkovski's formula.


Homework Equations


N/A. This is actually from differential equations textbook, and it did not give Ciolkovski's formula. I googled Ciolkovski's formula, but I am trouble finding it...


The Attempt at a Solution


I have no idea how to approach this problem. I do not have enough physics background knowledge to begin the problem :[ please help me...
 
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