# Intro to Differential Equations question.

• Aug 7th 2010, 11:26 AM
Suomik1988
Intro to Differential Equations question.
I've tried this problem a few times and am not sure if I actually got what they are asking for. I am in the process of latex-ing this out so I can put my work down here so you can see it. For now, here's the problem and of course any help is much much appreciated.

A skydiver with mass "m" jumps from a very large height. The only forces acting on him are the earth's gravitational pull (mg, where g=9.8m/s^2) and a retarding force due to air resistance, which is proportional to the velocity "v". Since F=ma and a=dv/dt, we then have the differential equation m(dv/dt)=mg-kv (k is constant)

I) Solve the differential equation for v.
II) Find the limit of v(t) as t approaches infinity, the skydivers terminal velocity.
• Aug 7th 2010, 11:57 AM
Ackbeet
Nice, clear presentation. Waiting to see what work you've done so far.
• Aug 7th 2010, 12:37 PM
chisigma
The second question has an immediate answer: the final velocity is the value for wich vanishes the 'combined force' and that happens if...

$\displaystyle \displaystyle m\ \frac{dv}{dt} = 0 \rightarrow v= \frac{m\ g}{k}$ (1)

Kind regards

$\displaystyle \chi$ $\displaystyle \sigma$