- #1
Matt Callicott
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Homework Statement
Find the distance, x, that an object of mass m travels through a medium, given an initial veloicty v0.
Homework Equations
I searched the web and came across a site that showed how to deal with velocity dependent forces. http://farside.ph.utexas.edu/teaching/336k/Newtonhtml/node17.html#svelyd
Equations:
FD = 1/2 ρCAv2 , simplified to FD = Bv2
mv (dv/dx) = -Bv2
The Attempt at a Solution
Going off of what the site said, I arrived at the following answer using these steps: mv dv = -Bv2 dx
(1/B) v/v2 dv = 1/m dx
-1/B ∫ 1/v dv = 1/m ∫ dx
-1/B ln(v / v0) = x / m
So this gives me that x = -m/B ln(v / v0)
However, this does not make since in the context of the question because x is dependent on v, which is not the initial velocity (v0). I do not know if my interpretation is wrong or if I am doing something wrong here. Any help is appreciated. Thanks