Can an object take off at a point A on the surface of the Earth and then land after some time only to land at a different place where it initially took off (because in the mean time the Earth has rotated while it was in the air)?
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If you were at the equator, your ground speed, due to the rotation of the Earth, is around 460 m/s (1 000 mph) so you are really moving.
Now say you jump into the air and somehow you delay your fall by 10 secs.
Will the earth have rotated a bit under you? No, because you have the same horizontal speed as you had on the ground.
This is why rockets are launched as near as possible to the equator, to add this rotational speed to their rocket engine provided speed. Nobody launches from the poles.