Jet engine: Frank Whittle (England) and Hans von Ohain (Germany) share inventor credit for the turbojet engine. English gov't and corporations punted on R&D, while germany committed a bit more resources.
Ballistic missile: We had an edge with Goddard's designs until about 1938. At that time, amateur societies in Germany, Russia and the USA were at a roughly even stage of development. Then the Germans did the same thing: commit R&D resources. It did help that they had a pair of engineering genii ("geniuses", ew) in the persons of von Braun and Riedel.
Once the war was over and the worth of the V2 was proven, especuially as a potential delivery means for the new bomb, both superpowers invested heavily in the development of large liquid-fueled ballistic missiles. The rest, as they say, is history.
A little something about Horten v. Northrop ...
http://www.schstwa2.tk/horten-bros-vs-northrop
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