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I am confused with a solution of momentum in Rocket problems which published and solved in "Fundamentals of Physics, (Halliday-Resnick)".

There are two different approachs to solving two similar questions. As i noticed, only difference is, the thing which flings. Fuel or tank(or any part of rocket). This is really confusing.

Say, the rocket and fuel total mass is "M", fired fuel mass "m" and "v" is first velocity of rocket plus fuel, relative to earth. The fuel is firing backward with "u" relative to rocket body. For earth final velocity of rocket body is "v'". The equation is;

M v = (M - m) v' + m (v - u) ....... (1)

But if the thing which throws backward is the empty fuel tank beside of fired fuel then equation is,

M v = (M - m) v' + m (v' - u) ....... (2)

highly similar. But notice the last parentheses. This questions are at the end of chapter 9. And the solutions are in the solutions book.

Chapter 9 - 6 : Preservation of Linear Momentum, exercises, question 15

and,

Chapter 9 - 7 : Practice of Momentum Principle, exercises, question 16.

these two questions are friend but equations not similar.

I am trying to guess about this difference but dont have any reasonable idea. Meanwhile, the questions,

9 - 7 - 18 (exercises): equation looks like (2) above

9 - 6 - 12 (problems) : equation looks like (2) above

are related too. Tired of thinking. Can you see the reason? Or any idea.

Note: This language is not my native for me. So, i tried my best for translating the name of chapters. BTW, i suppose the Chapter numbers are enough. If these explanations not enough then i will try to find them in English somewhere.

Have nice day