If it was recently thrown upward, it is either still travelling upwards away from the centre of the Earth, or it is falling downwards towards the centre of the

If it was recently thrown upward, it is either still travelling upwards away from the centre of the Earth, or it is falling downwards towards the centre of the Earth. So its past is kind of irrelevant. At some point if nothing is supporting it, it will fall towards the centre of the Earth. This is just high school physics.