I've been inspired by Ukelele Ike.
Given the fact the Gilligan's Island was probably the surrealest show ever put on the tube and thus was not designed to be scientifically (or otherwise) accurate; how many of the Professor's creations could he really have made with things he found around a tropical island.
F'rinstance, the pedal car seems plausible, as does the hot water plumbing system. The coconut phonograph doesn't (I think you'd have problems with the needle). We have lots of technical experts on this board, from engineers and chemists to tropical botanists. What could the Professor really have made?
Plunging like stones from a slingshot on Mars.