The door on an 'Uber for flying' private jet flew open shortly after it took off from San Francisco

Wheels Up, the "Uber for flying" as its CEO calls it, is a private jet service used by venture capitalists and wealthy families alike. It even shuttled around this season's Dancing with the Stars contestants.

However, despite touting its safety record in its September $115 million funding round, Wheels Up neglected to mention a scary incident involving one of its private planes.

On August 6, a Wheels Up flight took off from San Francisco en route to Michigan when a door opened shortly after take-off.

"Emergency! Our door flew off the aircraft," the pilot told air traffic controllers in a video posted to YouTube of the exchange. The two pilots and five passengers on board were all reported to be OK, but in the recording the pilot says, "they're gonna be pretty upset."

The plane couldn't climb to get out of the clouds or maintain its elevation, and it finally was able to turn around and make it back to land in San Francisco. There was one last complication though: The air traffic controller thought that the door hanging off of the plane was its landing gear and told them they only had one wheel down on the approach. (That turned out to be untrue.)

Wheels Up Executive Vice President of Safety, Dave Hewitt, told Business Insider in an email that the plane door remained attached to the plane, but couldn't comment further because of the investigation.

"As is typical with aviation events, Wheels Up cannot provide any information while an FAA review is underway.  However, we can confirm that the main entry door of the aircraft remained attached throughout the flight in question," Hewitt said. "Wheels Up has set, and continues to maintain, the highest safety and pilot training standards in the private aviation industry, based on decades of experience and robust safety management system principles."

You can listen to the whole exchange in this video. The emergency call starts around the one-minute mark:

It's not the first time a plane door has opened while in the air. In July, a passenger in Malaysia filmed a door of plane hanging open during a regional flight.