# Integration question from book “e: The Story of a Number” by Eli Maor [closed]

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 Sklivvz♦, Manishearth♦Dec 29 '12 at 15:56

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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