relative motion - Does being suspended in air allow you to not be affected by Earth's rotation?

Let's assume that there was some mechanism by which we could remain suspended in air. By this I mean that our feet is not in contact with the ground. One possible way of doing this would be by means of a jetpack. If we could remain suspended in air for a while in this manner, will we be in a different place when we come down, due to the Earth's rotation? When I thought of this problem in the micro scale using a ball (which rotates), it appears like I'll be in a different place when I come down from my suspended state. Am I overlooking something here?