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?
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: : 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) ?
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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.