It's a Bird, It's a Plane Gilligan's Island : Season 3 Episode 27

A U.S. Air Force jetpack washes ashore in the lagoon. After close inspection of the jetpack, the Professor determines that the tanks contain just enough fuel to carry Gilligan to Hawaii. However, that determination was made before Gilligan wasted most of the fuel while proceeding to goof-up several attempts to be discovered and rescued. While flying the jetpack near where Navy search vessels are reported to be lurking, Gilligan is so scared by a radio report of an ""Unidentified Flying Object in the area"" that he blasts higher and hides in a cloud, not realizing that the UFO the Navy ships see is actually him with the jetpack!