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what did I do wrong on this one?

Mathematics
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which one?
Answer is \[v_f-v_i=-u \ln (\frac{m_f}{m_i})\]I have no idea where the negative sign comes from. Here's what I did:\[m \frac{dv}{dt}=u \frac{dm}{dt}\]where u is a constant. so,\[dv=u \frac{dm}{m}\]and integrating:\[v_f-v_i=u \ln (\frac{m_f}{m_i})\]I don't know where the negative sign come from....
you seechange in velocity dv is positive quantity whereas change in mass is negative

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Other answers:

yeah the negative sign makes it work, and I agree it needs one. I just don't know how to justify it mathematically.
ots because u should have had -ve sign in rhs from the first equation onwards!!
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ok....it's confusing the way the instructor wrote it. If there were vector signs on v and u then it would make sense to add the negative sign once the vector arrows were dropped since v and u are in opposite directions. The instructor didn't do this though. Ok, thanks!
welcome!

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