When the bazooka was born, it combined two cutting-edge technologies: the rocket and the shaped-charge warhead.
When the US sent bazookas to its comrades on the eastern front, they fell into German hands.
The Germans quickly developed the Panzerfaust (“tank fist”) and then the Panzerschreck (“tank fright”).
The Panzerschreck was a bazooka, scaled up to 88 mm — a successful caliber for the Germans. The earlier Panzerfaust though was something different: a cheap, single-shot, “recoilless rifle” — in the same family as the modern M3 Carl Gustaf, the Goose. So, the Panzerfaust did use a shaped-charge warhead, which could penetrate armor even at low velocity, but it didn’t use a rocket to propel it. In fact, it used 830 grains of black powder.
In movies, the modern RPG is often depicted traveling at low speed, when in real life its gunpowder booster charge launches it out of the barrel at 115 m/s, and then its rocket engine kicks it up to 295 m/s (660 mph). The original Panzerfaust actually did travel at thrown-ball speeds though: 30 m/s (67 mph).
While the rocket-propelled device was developed in the USA, the shaped-charge was developed simultaneously in Germany and the UK in the 1930s, and later adopted by the USA in the 1940s:
(Source: GlobalSecurity.org)