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Math Help - unnecessary hyperbole?

  1. #1
    Member billym's Avatar
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    unnecessary hyperbole?

    ma = mg - kv^2<br />


    I have to find v in terms of t so I used the substitution
    <br />
\frac{dv}{dt} = a<br />

    <br />
\int \frac{1}{g - kv^2} \, dv<br />

    where:
    <br />
 k = \frac{0.2D^2}{m}<br />

    I'm not terribly fond of the "ArcTanh" result... is there another way to do this?
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by billym View Post
    ma = mg - kv^2<br />


    I have to find v in terms of t so I used the substitution
    <br />
\frac{dv}{dt} = a<br />

    <br />
\int \frac{1}{g - kv^2} \, dv<br />

    where:
    <br />
 k = \frac{0.2D^2}{m}<br />

    I'm not terribly fond of the "ArcTanh" result... is there another way to do this?
    Well assuming k \ge 0 partial fractions look promising.

    (by the way if this is supposed to be motion under gravity in a resisting
    medium this is only valid if the axis system is positive downwards and the
    intial velocity is zero or positive - but assuming high Reynold's number,
    a sky diver perhaps).

    RonL
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