The Boeing 737 had 143 people on board and had taken off from Guantanamo Bay, Cuba.
The footage was taken after all the people had made it off the Miami Air military charter, 22 people were hurt, but their injuries were not serious.
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One of the officers is heard saying "wow."
There were heavy thunderstorms in the area when the jetliner came in to land.
The National Transportation Safety Board is investigating the crash and it could take 18 months before it reaches a conclusion.
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