How Does the Coriolis Force Affect a Northbound Plane's Flight Path?

[karnten07]

Homework Statement

A plane with a fully laden mass of 500 tonnes is flying due north at a steady speed of 1000kmh^-1 and is located at a latitude of 51 degrees north at a specific time.

What force in an east-west direction is required to keep the plane on course along a fixed line of longitude.

Homework Equations

The Attempt at a Solution

So due to the inertial effect of the Coriolis force, the plane requires a force acting east to keep it on a fixed line of longitude because the coriolis force is acting west on the plane.

The magnitude of the coriolis force is given by this equation:

mx'' = -2mw(z'cos(theta) - y'sin(theta))

where x is the east direction , z is vertically up, y is north, theta is the latitude

So in this case, because there is no velocity in the z direction, it becomes:

mx'' = -2mw(-y'sin(theta))

Is this right?

 

[karnten07]

Hi guys, i think I've got this right, but I am not entirely sure, i get a force of 16000 N.