# Coriolis Force Along the Surface of the Earth

## Homework Statement

I don't want to post the actual question because I want to understand the situation in a general case. Basically, there is a bullet that moves south along the surface of the Earth as in this diagram: http://abyss.uoregon.edu/~js/images/coriolis_effect.gif. You have to find the deflection from the target.

## Homework Equations

Newton's Second Law in a Non inertial frame, Coriolis Force

## The Attempt at a Solution

I don't have a solution becasue I can't understand what's going on. In my textbook, they set up a "local coordinate system" that moves along the surface of the Earth like this: http://i.imgur.com/Eyhq1WF.png. I want to understand why and how they can do this.

I haven't worked out the actual direction of the deflection, but I assume from the picture above it would be westward. If the coordinate system moves along the Earth, can you write a simple DE like $$\ddot{y}=\text{Coriolis Acceleration in this Direction}$$ ? I don't think you can since the latitude changes as you move south.