# Re: DE word problem

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Posted by Subhotosh Khan on September 04, 2002 at 08:31:09:

In Reply to: Re: DE word problem posted by colin on September 03, 2002 at 17:29:10:

: : : A body with mass m is projected vertically downward with initial velocity v0 in a medium offering resistance proportional to the square root of the magnitude of the velocity. Find the relation between the velocity v and the time t.

: : : Do I solve for v or t here? How can I tell?
: : *******************************************
: : You need to find a function V(t) - Velocity as a function of time, from the following physical equation:

: : Acceleration = dv/dt = g - k*sqrt(v)
: : Where:
: : g = acceleration due to gravity
: : k = proportionality constant

: what happened to the mass m?
: Shouldn't it be:
: dv/dt = g - k/m * sqrt(v) ?

********************************************
Assuming that this is a problem where mass is constant, you can absorb that in your proportionality constant. In other words,

Drag = k_1 * sqrt(v) and

k = k_1/m

Incidentally, mass will not be constant when you are looking at a accelerating rocket. The spewing fuel will change the mass. Of course, then the problem becomes quite complicated - and you will need a rocket scientist to solve it.

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