The cat is fine. Otherwise, this video would be terrible.
I’m guessing poor kitty fell asleep and awoke to a huge shock. I’ll just let the video speak for itself. 
Kitty goes for ride.
Ongoing thread: An unexpected passenger (airplane) - Miscellaneous and Personal Stuff I Must Share - Straight Dope Message Board
Since there is another discussion going on in the thread linked above I’m going to close this.