Drag equation and d(kinetic energy)/d(displacement)

[Tiiba]

Homework Statement

Given the drag equation and a projectile's initial kinetic energy and mass, find the distance in which it will come to rest (or at least, become absurdly slow).

Homework Equations

https://en.wikipedia.org/wiki/Drag_equation

The Attempt at a Solution

Force = .5 * fluid density * drag coefficient * area * velocity^2.
Velocity = sqrt(2 * energy / mass)
Force = fluid density * drag coefficient * area * energy / mass.

When the bullet emits dE energy, it travels dE/F.

Thus, position delta = dE/dP = dE/F = dE / (fluid density * drag coefficient * area * energy at step / mass)

dE/dP = (mass / (fluid density * drag coefficient * area)) 1/E dE

Everything in front of 1/E is a constant, so it isn't integrated. The integral of 1/E is ln(E), so the solution is

displacement = (mass / (fluid density * drag coefficient * area)) (log(E0) - log(1 eV))

4. ?

WTF is ln(E)?

 

[Dr. Courtney]

Your notation is a mystery.

 

[Tiiba]

What in particular? I just took the drag equation and rearranged it. I want to figure out how far the projectile moves based on its mass and speed. How would you do it?