Buoyant Cork

The diagram shows a bucket filled with water hanging on a string, with a cork tied to the base of the bucket by another string.

When the cork's string is cut, since the cork is less dense than water, the cork will rise up due to buoyancy.

When the string holding the bucket is cut, the bucket and its contents will fall due to gravity.

What happens if both strings are cut simultaneously? How would the cork move relative to the bucket?

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