The pilots of a Southwest airplane that landed at the wrong Missouri airport have been placed on leave as federal officials continue to look into what caused the mistake. NBC's John Yang reports.

Southwest Airlines on Monday grounded the two pilots who landed a passenger jet at the wrong Missouri airport — disturbingly close to a dropoff at the end of the runway, according to one passenger.

The pilots have been put on paid leave until a federal investigation into the incident — the second such mixup in two months — is completed.

The Boeing 737-700, carrying 124 passengers and five crew from Midway Airport in Chicago, was scheduled to touch down at Branson Airport on Sunday. Instead, it made a surprise landing at M. Graham Clark Downtown Airport, which is primarily used by corporate, charter and personal aircraft.

Federal Aviation Administration spokesman Tony Molinaro says the agency is investigating the incident. The National Transportation Safety Board plans to interview both pilots by Tuesday and will analyze the black boxes.

No injuries were reported during the mix-up, but passengers said the landing was jarring.

"He braked very hard," Dallas estate attorney Scott Schieffer told NBC News. "We could smell burnt rubber from inside the airplane."

"The flight came to a very abrupt end, almost like a crash," Diane Coplan told told NBC affiliate KXAS. "It just dropped to the ground and all of our bodies were accelerating forward very fast. You're holding on to the seat in front of you, not knowing what was happening."

Five minutes later, the pilot announced on the public address system that they had landed at the wrong airport.

"He said they were close, but it's nine miles away," Schieffer said.

"It's not like they’re right next to each other. It was dark at that time, but I was like, 'How does this happen?'"

Related: Passengers recount bumpy landing

Because the downtown airport was not equipped to handle the Southwest flight, passengers were kept on the plane for 90 minutes while buses were sent to the tarmac, Schieffer said.

When they deplaned, he said, he got his second shock of the night — the plane was less than 200 feet from a dropoff at the end of the runway.

"A local official said, 'Son, look 40 feet behind those buses. You would have gone off that cliff,'" Schieffer recalled.

Here's the end of the runway that we braked hard to avoid on @SouthwestAir 4013. pic.twitter.com/c9A4oHRpps — Scott Schieffer (@ScottDallasTX) January 13, 2014

It took an hour for the buses to bring everyone to the correct airport and another two hours to get them on a plane to Dallas.

"People were just exhausted," he said.

He said passengers were given a $200 flight voucher but no real explanation for the snafu. The pilots stayed in the cockpit when everyone was getting off.

"What I'd like to find out eventually is how did this happen," he said.

Southwest said in a statement that it is cooperating with investigators.

Tom Kreamer, a veteran commercial pilot and senior consultant for for Safety Operating Systems, said his first question would be whether the pilots were using electronic guidance for the landing — and if not, why.

"It’s fine to do visual approaches and visual landings, but use the electronic guidance as a backup," Kreamer said.

He said investigators will also be looking at the weather and light conditions at the time, any contact between the cockpit and air traffic control, and what type of clearances the crew was given.

The incident was the second in two months in which a plane has arrived at the wrong destination. In November, a behemoth Boeing air freighter set down at a small airport in Wichita, eight miles from its intended destination at McConnell Air Force Base.

In that case, officials had to shut down a highway and roads near the airport as a safety precaution to allow the plane to take off from a shorter runway the next day.

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