A hinge is supporting a door that is hanging down from it (think of a doggie door). When a wind is blowing at the top of the hinge at a constant 11 m/s the door is perfectly horizontal (in the beginning it was perfectly vertical with no wind). If a wind of 11 m/s is needed to rotate the door on the hinge 90 degrees, how fast should the wind blow for the door to rotate only 30 degrees? No weight or length is given and the hinge is frictionless. Again, the wind is blowing at the top of the hinge, not directly at the door. Any help would be greatly appreciated.

I'm not sure I understand what the situation is. The wind is blowing at the top of the hinge only? I don't think that would do anything to the door...

Yeah makes no sense.

Force need to act upon door, not hinge

Well if the wind blows on the hinge... which makes little sense... you are going to use leverage

Lever arm(length) multiplied by force of wind which will give you the torque on the door.
BUT

I think you meant the wind is blowing at the bottom of the door. Lever arm would be length of door plus radius of hinge multiplied by wind