Question

what did I do wrong on this one?

Answer 1

which one?

Answer 2

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....

Answer 3

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

Answer 4

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

Answer 5

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