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Math Help - more inegration

  1. #1
    Member billym's Avatar
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    more inegration

    I need to solve for v... not a clue...

    <br />
\frac{dv}{dt} = -\frac{g}{b^2}(v^2 + b^2)<br />
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  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
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    Quote Originally Posted by billym View Post
    I need to solve for v... not a clue...

    <br />
\frac{dv}{dt} = -\frac{g}{b^2}(v^2 + b^2)<br />
    This is a seperable equation

    <br />
\frac{dv}{v^2+b^2} = -\frac{g}{b^2}dt<br />

    Now we integrate both sides

    <br />
\int \frac{dv}{v^2+b^2} = \int -\frac{g}{b^2}dt \iff \frac{1}{b^2} \int \frac{dv}{1+(v/b)^2}=  - \frac{g}{b^2} \int dt \ =

    \int \frac{dv}{1+(v/b)^2} = -g \int dt<br />
    finally we take the integral and we get

    b \tan^{-1}(\frac{v}{b})=-gt+c

    Now all you need to do is solve for v.

    Good luck
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