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GR8677 #62
Problem
 GREPhysics.NET Official Solution Alternate Solutions

Mechanics$\Rightarrow$}Separable Differential Equations

Solve $m\frac{dv}{dt}=-u\frac{dm}{dt}$. Separate variables to get \par
$\int u\frac{dm}{m}=\int -dv\Rightarrow u \ln (m_0/m)=v(t)$. None of the answer choices such a ln relation for $v$, and thus the answer is (E), none of the above.

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Comments
deneb
2018-10-10 04:15:46
well damn, didn\'t think about E, I solved the equation and saw \"ln\" so I just picked B lol
lattes
2008-08-06 13:19:11
Another way to solve is considering $m=m_{0}$ on the choices. None of them gives $v=0$ so the answer must be (E)
 chrisfizzix2008-10-03 13:21:18 This man speaks the truth. Solving a DEQ no matter how simple is almost always not the way to go about solving an ETS problem. Boundary conditions are definitely the way to go here.
 shak2010-07-31 13:03:10 in this problem, boundary condition works very good, right:) and also we can always check solution by initial and boundary condition, and eliminate wrong answers
Blake7
2007-07-22 20:55:16
Why would someone attempt a "None of the above" problem on a timed record exam? I see that and think "BYPASS" immediately.

 Rune2007-10-14 22:51:00 Because in this case it is very simple as long as you know the $\int \frac{1}{x}dx$, in which case it takes all of 15 seconds to read and solve.
 gliese876d2008-10-17 11:26:40 Or because, crazy lunatics like me actually had the eq. for this memorized, so it took 2 seconds to realize the right answer wasn't there :)
 neon372010-11-03 10:18:31 None of the above in this was pretty easy to figure but, it was very hard to be quite confident. I must remember use boundary conditions!! It is the way to go for ETS DEQs.
 llama2013-10-16 18:47:14 Or these days, because you play kerbal space program and have an interest in physics so you know the rocket equation

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LaTeX syntax supported through dollar sign wrappers $, ex.,$\alpha^2_0$produces $\alpha^2_0$. type this... to get...$\int_0^\infty$$\int_0^\infty$$\partial$$\partial$$\Rightarrow$$\Rightarrow$$\ddot{x},\dot{x}$$\ddot{x},\dot{x}$$\sqrt{z}$$\sqrt{z}$$\langle my \rangle$$\langle my \rangle$$\left( abacadabra \right)_{me}$$\left( abacadabra \right)_{me}$$\vec{E}$$\vec{E}$$\frac{a}{b}\$ $\frac{a}{b}$

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