anonymous 3 years ago what did I do wrong on this one?

1. anonymous

which one?

2. anonymous

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....

3. AravindG

you seechange in velocity dv is positive quantity whereas change in mass is negative

4. anonymous

yeah the negative sign makes it work, and I agree it needs one. I just don't know how to justify it mathematically.

5. AravindG

ots because u should have had -ve sign in rhs from the first equation onwards!!

6. AravindG

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7. anonymous

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!

8. AravindG

welcome!