Cork In Bucket

A cork, say from a wine bottle, is held by a robotic clamp at the bottom of a bucket of water and released the moment the bucket is dropped off the side of a tall building. What will happen to the cork during the fall? Will it float to the top of the bucket normally, slower than normal, faster than normal, or not at all?
Assume that there is no air resistance to slow the bucket down.

The cork will stay at the bottom of the bucket and not float up at all during the fall, since the cork, the bucket and the water all fall at the same acceleration (neglecting air resistance as all good Physics questions do). The buoyant force of the water does not push the cork upward in this case since in free fall the buoyant force is zero. In other words, a cork only floats up when the water around it is heavier and pushes it up. In free fall the water is weightless, as is the cork and the bucket. So, there is no force to push the cork to the top of the bucket.

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