GREPhysics.NET: GR8677 #62

GR8677 #62

Problem

GREPhysics.NET Official Solution

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

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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)

chrisfizzix
2008-10-03 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.

shak
2010-07-31 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

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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.

Rune
2007-10-14 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.

gliese876d
2008-10-17 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 :)

neon37
2010-11-03 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.

llama
2013-10-16 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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Bare Basic LaTeX Rosetta Stone
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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