Neither United nor the FAA indicated anyone was injured on United Flight 1722 on Dec. 18.
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The plunge occurred a little over a minute after takeoff, the data show.
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The plane lost more than half its altitude and came within 775 feet of sea level, according to the data from FlightRadar24.
The plane gained speed as it dropped 1,425 feet from 2,200 feet before regaining its climb out of Kahului on the island of Maui.
'Felt like ... a roller coaster'
Rod Williams II and his family were sitting near the back of the plane when the Boeing 777 made a terrifying plunge shortly after taking off from Kahului Airport in Hawaii.
Williams told CNN the plane seemed to be flying normally at first, but then he said the plane climbed at "a concerning rate" for a few seconds.
"It felt like you were climbing to the top of a roller coaster. It was at that point," Williams said. "There were a number of screams on the plane. Everybody knew that something was out of the ordinary, or at least that this was not normal."
The plane then went into a "dramatic, nose-down" dive for about eight to 10 seconds before it climbed steeply again and resumed normal flight.
United said it conducted an investigation with the FAA and the pilots union "that ultimately resulted in the pilots receiving additional training," adding the investigation is ongoing.
The pilots have a combined 25,000 hours of flight time.
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"The United Airlines flight crew reported the incident to the FAA as part of a voluntary safety reporting program. The agency reviewed the incident and took appropriate action," the FAA told CNN.
Although the weather at the exact time is unclear, the National Weather Service reported the day set a daily record for rainfall at Kahului.
The incident, which is coming to light only now, was first reported by the website Air Current.
'You're just kind of gripping the seat'
The experience was harrowing for passengers.
"When the plane started to nosedive, multiple screams are being let out, at that point," Williams said. "You're trying your best to maintain your composure -- there's obviously kids on the flight -- nobody really knows what's going on, but at the same time, you're concerned. You don't know if this is an issue, but it was certainly out of the ordinary."
Williams said he and his wife were sitting on either side of their children and glanced at each other during the steep descent.
"It's tense, you don't really have a chance to speak or to conjure up words, you're just kind of gripping the seat and praying under your breath," he said. "I asked her later and sure enough ... we were praying for a miracle, because we felt like this could be it."
Flight attendants comforted some passengers after the incident and there was an announcement on the loudspeaker about 10 minutes later.
"Someone from the cockpit got on the intercom and said, 'Alright, folks, you probably felt a couple G's on that one, but everything's gonna be OK. We're gonna be alright,' " Williams said.
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Williams studied aviation in college, so he had some idea of what was happening, but his daughter, 10, and son, 7, had never flown before their trip to Hawaii, so they didn't really know what was happening. They were scared, Williams said, but his son still wants him to play United by flying him on his shoulders.
The rest of the flight went smoothly, but Williams said there was a strong crosswind when they landed in San Francisco. They then took another flight home to Ohio.
Williams wasn't aware of how close the plane came to the water until Sunday night -- eight weeks after the flight -- when his father showed him the report on the incident.
Williams said he has tried to focus on the wonderful memories they made on what he called a once in a lifetime vacation and that he didn't want his kids to be afraid to fly so they can enjoy future trips.
"Now that I know, statistically what had happened, and that we were about 5 to 5.2 seconds from hitting the water, you know, I'm definitely counting my blessings," he said. "I'm reminded that when my wife and I pray together before the flights that, you know, there's a God that's here in that."
He said he was grateful for the pilots' "amazing, amazing recovery efforts," and said they should be praised for that.
"You read about these things, but then when you get to experience it, it's just, sobering, you know. I'm very thankful to be here today."
The-CNN-Wire
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