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Math Help - Intro to Differential Equations question.

  1. #1
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    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.
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  2. #2
    A Plied Mathematician
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    Nice, clear presentation. Waiting to see what work you've done so far.
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  3. #3
    MHF Contributor chisigma's Avatar
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    The second question has an immediate answer: the final velocity is the value for wich vanishes the 'combined force' and that happens if...

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

    Kind regards

    \chi \sigma
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