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The passenger killed has been identified as a mother of two who was also a Wells Fargo bank executive from New Mexico.
News of Jennifer Riordan's death was first shared by the assistant principal of the Albuquerque Catholic school attended by her two children.
Passenger on Southwest plane that made emergency landing: We started saying our goodbyes
In an email to parents, assistant principal Amy McCarty wrote that "the family needs all the prayers we can offer."
Riordan was a vice president of community relations for Wells Fargo bank. She was the wife of Michael Riordan, who served until recently as the chief operating officer for the city of Albuquerque.
The New Mexico Broadcasters Association on social media said Riordan was a graduate of the University of New Mexico and former board member.
Travelers said fellow passengers dragged the unidentified woman back in as the sudden decompression of the cabin pulled her part way through the opening.
The pilot of the plane, a twin-engine Boeing 737 bound from New York to Dallas with 149 people aboard, took it into a rapid descent and made an emergency landing in Philadelphia as passengers using oxygen masks that dropped from the ceiling said their prayers and braced for impact.
"I just remember holding my husband's hand, and we just prayed and prayed and prayed," said passenger Amanda Bourman, of New York. "And the thoughts that were going through my head of course were about my daughters, just wanting to see them again and give them a big hug so they wouldn't grow up without parents."
"I am immensely grateful that there are no other reports of serious injuries, but this is a tragic loss," Southwest Airlines CEO and chairman Gary Kelly said at an evening briefing.
Kelly did not name the pilot but said he was an experienced airman, who has been with Southwest since 1994.
"Our hearts go out to the family of that deceased customer," Kelly said.
Another passenger, Alfred Tumlinson, of Corpus Christi, Texas, said a man in a cowboy hat rushed forward a few rows "to grab that lady to pull her back in. She was out of the plane. He couldn't do it by himself so another gentleman came over and helped to get her back in the plane and they got her."
Another passenger, Eric Zilbert, an administrator with the California Education Department, said: "From her waist above, she was outside of the plane."
Passengers commended one of the pilots for her cool-headed handling of the emergency. She walked through the aisle and talked with passengers to make sure they were OK after the plane touched down.
"She has nerves of steel. That lady, I applaud her," Tumlinson said. I'm going to send her a Christmas card, I'm going to tell you that, with a gift certificate for getting me on the ground. She was awesome."
National Transportation Safety Board chairman Robert Sumwalt said one person died, but he gave no details. It was the first passenger fatality in an accident involving a U.S. airline since 2009.
The NTSB sent a team of investigators to Philadelphia. Sumwalt said the engine will be taken apart and examined to understand what caused the failure.
Photos of the plane on the tarmac showed damage to at least one window and a chunk missing from the left engine, including part of the engine cover.
Philadelphia Fire Commissioner Adam Thiel said there was a fuel leak in the engine when firefighters arrived and a small fire was quickly brought under control.
Bourman said she was seated near the back and was asleep when she heard a loud noise and oxygen masks dropped. She said the plane was fairly quiet because everyone was wearing a mask.
"Everybody was crying and upset," she said. "You had a few passengers that were very strong, and they kept yelling to people, you know, 'It's OK! We're going to do this!'"
In a recording of conversations between the cockpit and air traffic controllers, an unidentified crew member reported: "We have a part of the aircraft missing, so we're going to need to slow down a bit." She also said that there was a hole in the plane and that she was told "someone went out."
After the plane landed, a woman was hospitalized in critical condition, and seven others were treated for minor injuries, authorities said.
Passenger Marty Martinez went on Facebook Live while wearing an oxygen mask. He posted, "Something is wrong with our plane! It appears we are going down! Emergency landing!! Southwest flight from NYC to Dallas!!" After the plane landed, he posted photos of a broken window near the left engine.
Everyone started yelling to brace for impact as the plane came in for a landing, Bourman said. She said passengers clapped and praised the pilot after the aircraft touched down.
"We were very lucky to have such a skilled pilot and crew to see us through it," Zilbert said. "The plane was steady as a rock after it happened. I didn't have any fearing that it was out of control."
Bourman said she saw emergency workers using a defibrillator to help a woman who was then taken off the plane. Bourman said that she also saw a man in a cowboy hat rush to cover the broken window and that the man had a bandage around his arm after the plane landed.
Passengers did "some pretty amazing things under some pretty difficult circumstances," Thiel said.
Tracking data from FlightAware.com showed Flight 1380 was heading west over Pennsylvania at about 32,200 feet (10 km) and traveling 500 mph (800 kph) when it abruptly turned toward Philadelphia.
The last time a passenger died in an accident on a U.S. airliner was 2009, when 49 people on board and one on the ground were killed when a Continental Express plane crashed on a house near Buffalo, New York.
Southwest has about 700 planes, all of them 737s, including more than 500 737-700s like the one in Tuesday's accident. It is the world's largest operator of the 737. The 737 is the best-selling jetliner in the world and has a good safety record.
Kelly said at a news conference in Dallas that there were no problems with the plane or its engine when it was inspected Sunday.
The jet's CFM56-7B engines were made by CFM International, jointly owned by General Electric and Safran Aircraft Engines of France.
CFM said it sent experts to help NTSB investigators. In a statement, it said the CFM56-7B has had "an outstanding safety and reliability record" since its debut in 1997, powering more than 6,700 aircraft worldwide.
"I spoke with the FAA the USDOT and NTSB to assure them that they have our full attention and cooperation," Kelly said.
Last year, the engine maker and the Federal Aviation Administration instructed airlines to make ultrasonic inspections of the fan blades of engines like those on the Southwest jet. The FAA said the move was prompted by a report of a fan blade failing and hurling debris. But it was unclear whether the particular engine that failed on Tuesday was covered by the directives.
"There's a ring around the engine that's meant to contain the engine pieces when this happens," said John Goglia, a former NTSB member. "In this case it didn't. That's going to be a big focal point for the NTSB - why didn't (the ring) do its job?"
Goglia said the Boeing 737 is a safe plane but engine failures happen from time to time.
"We're pushing the engines to produce as much power as possible," he said. "We're right on the edge. Sometimes they fail, and that's why the containment ring is there."
In August 2016, a Southwest Boeing 737-700 jet blew an engine as it flew from New Orleans to Orlando, Florida, and shrapnel tore a 5-by-16-inch hole just above the wing. The plane landed safely. The NTSB said a fan blade had broken off, apparently because of metal fatigue.
Before Tuesday, Southwest had never had an accident-related fatality of a passenger, although a boy died in 2006 when a Southwest jet skidded off a runway at Chicago's Midway Airport, crashed through a fence and collided with the boy's family's car.