Tell me more ×
Physics Stack Exchange is a question and answer site for active researchers, academics and students of physics. It's 100% free, no registration required.
up vote 1 down vote favorite

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?

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

share|improve this 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

closed as too localized by Sklivvz♦, 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, see the FAQ.