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In the book 'e: The Story of a Number', a derivation of a parachutist problem is given on pg. 109-110. A parachutist jumps from a plane and at $t=0$ opens his chute. At what speed will he reach the ground?

$k$ is proportionality constant. $g$ is acceleration of gravity. $m$ is mass of parachutist. (This derivation assumes air resistance is linear with velocity.)

I am able to follow the derivation up to equation 3.

$$\tag{1}m\frac{dv}{dt} = mg - kv$$

$$\frac{dv}{dt} = g - av \tag{2}, \quad a = \frac{k}{m}$$

$$\frac{dv}{g-av} = dt \tag{3}$$

How does one integrate (3) to get the following?

$$-\frac{1}{a}\ln|g-av| = t + c \tag{4}$$

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closed as too localized by Ebenezer Sklivvze, Manishearth Dec 29 '12 at 15:56

This question is unlikely to help any future visitors; it is only relevant to a small geographic area, a specific moment in time, or an extraordinarily narrow situation that is not generally applicable to the worldwide audience of the internet. For help making this question more broadly applicable, visit the help center.If this question can be reworded to fit the rules in the help center, please edit the question.

    
Make the change of variable in eq 3 as: $g-av=z$, then differentiate both sides and express the left hand side in terms of the new variable $z$. –  Antillar Maximus Dec 23 '12 at 16:37
    
This question currently has no real value to future visitors, so I'm closing this. –  Manishearth Dec 29 '12 at 15:56