Imagine a remote controlled toy helicopter vertically takes off from a table and hovers at about one metre over the table that is of one metre height: hence, the total altitude is 2 metres.
What will it do if it is moved away from over the table at the same altitude?
Will it hover at the same altitude ( with respect to the floor: i.e. 2 metres)?
Or, will it fly down and hover at about one metre above the floor (the total altitude - the height of the table)?
Ignoring more complicated effects of flow, which are only relevant very close to the ground, the helicopter is hovering not because it is pushing itself away from what's beneath, but due to accelerating air downwards, which, due to conservation of momentum, causes an equal force on the helicopter, but in the opposite direction. This does not depend on its distance to the floor (again, neglecting effects that only matter in extreme cases, high or low). Therefore, removing the table should not affect the height.
If this were different, and the helicopter would always adjust its height to the ground, flying above a city would be really hard: Every building would cause you to drop or rise dramatically.
