# Math Help - unnecessary hyperbole?

1. ## unnecessary hyperbole?

$ma = mg - kv^2
$

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

$
\int \frac{1}{g - kv^2} \, dv
$

where:
$
k = \frac{0.2D^2}{m}
$

I'm not terribly fond of the "ArcTanh" result... is there another way to do this?

2. Originally Posted by billym
$ma = mg - kv^2
$

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

$
\int \frac{1}{g - kv^2} \, dv
$

where:
$
k = \frac{0.2D^2}{m}
$

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