Thread: Rotating Frames of Reference

Ok so i've been given two versions of a problem dealing with rotating reference frames in classical mechanics, one was on an assignment and the other was just yesterday on a mid-semester exam. I can't seem to work this one out, even though i'm sure there's something simple i'm not considering.

The Question:
An object is dropped from a tower that is 50m in height and located at a lattitude of 45 degrees North. Consider only the forces of gravitation, the centrifugal force and the coriolis force to find the deflection of the objects trajectory in the East-West and South-North direction.

so first i mindlessly applied an equation dealing with the relationship between accelerations observed by an inertial observer (O) and a non-inertial observer (O'). That being,



So in cylindrical coordinates i'm left with,



Solving for the inertial case,

So at impact, ie. when the flight time is calculated to be,

Using this result we find that just before the object hits the ground,



My main problem is with what to do about the coriolis term, assuming i haven't buggered the whole thing up.