Hovering around a spinning Planet with no Atmosphere If you imagine standing on some spinning planet with no atmosphere, and you had some jet pack that allowed you to hover above that planet:

Would you land at the same spot that you took off? 

On one hand, your inertia will keep you moving and you'll have a purely normal force everywhere, so you shouldn't speed up (am I mistaken). So you will just end up rising and falling in the frame of the planet (do we need to include a coriolis force?)
On the other hand, your angular velocity will be slower than that of the planet- so as you rise higher and higher; you should fall behind. 
Can anybody give me an answer, preferably including the mechanics here. To be clear; the only forces are the gravity and the upward force of the jet pack. 
 A: If you lock your rocket's gyros in pure vertical angle and start from somewhere on the equator, you will move up and back with the ratio of omega/omega_(0) = r/(r+h), falling behind. 
Where r is radius of planet and h is you altitude above surface. 
Also if you go high enough you have to calculate and manouver to be able to com back at where you took off.
Also things change if you take off from a different latitude. Like if you take off from say the planets north pole, you keep going up straight and will come back straight easily.
If you take off from say 45° latitude the lagging in omega will be a mixture of  several orbital effects.
A: Assuming you were to jump (forget jet pack for now) you will land at the same spot due to the following:
As you rise to a certain height you will get behind by a given amount, the higher you go the bigger the amount, but when you come back down you will speed up and the amount will reduce to zero thereby landing on the same spot.  You need to jump as if you were standing on a frictionless surface otherwise you could jump out of the plane of rotation. You do not need to worry about coriollis because you are in the plane of rotation.
One reason the jet pack will not work is because as you use it your mass is decreasing which changes your angular velocity. But let's assume you have magic jetpack, the problem is your use of the word hovering which implies using additional force once you have left the planet surface.  All the energy used hovering is separating you from the planet, you could potentially use some of that energy to keep up to the spot, or get ahead of it or fall behind.
