The woman died, officials said.
The woman was sitting on the left side of the plane when something in the engine apparently broke and smacked into the window. She hung out the hole for many minutes, said Hollie Mackey, who sat next to the victim, and Amy Serafini, who was in the row behind the woman.
Many passengers kept trying to pull the woman back into the plane for a long time, until two men were able to get the woman back in her seat, they said.
A nurse answered a call for help and tried to do CPR.
Investigators from the National Transportation Safety Board got a preliminary look at the engine that failed.
One of 24 fan blades was missing, NTSB Chairman Robert Sumwalt said in Philadelphia.
Sumwalt said a first look showed there was evidence of metal fatigue where the blade attached to a hub.