I think one of the LSR cars now being built is going to use rockets and a jet engine.
The JATO bottles used to help get the downed-pilot search plane Grumman PBY Catalinas (the entire wing was a giant gas tank, allowing them to remain aloft for thousands of miles, but necessitated 'help' getting underway: the JATO rockets) into the air during WW II were designed by Dr. Robert H Goddard, "Father of American Rocketry," whose work was largely ignored by the American military during the period between WW I-WW II. A member of the Dupont family privately invested in Goddard's work, allowing him to continue to develop the liquid-fueled rocket. His work and launches, and crash landings on the East Coast caused much complaining, and he was able to use the Dupont funds to relocate to the American Southwest, where he had more room to avoid an errant rocket crashing and doing damage.
One group that
did pay attention to Goddard's research, which he painstakingly documented and published in a flurry of scientific papers, was the Nazi party. They used Goddard's research to develop their own programs, principally under Hermann Oberth (Werner von Braun was a student who helped Oberth's research) which years later resulted in one of the most terrifying aerial weapons of WW II, the A4/V2 liquid-fuelled rocket. They also had a pilotless ram-jet that was much more-simple, cheaper, and crudely effective, the V1 'buzz-bomb.' Both these were used to bomb Great Britain.
Solid fuel rockets were used by Germans to propel cars between the world wars, in a quest for speed. Doesn't Fritz von Opel look dashing? Yes he of the Opel car co. family. Dig the wing on the car, perhaps one of the earliest uses of automotive downforce devices. The Rumpler from the time of WW I was another aerodynamic groundbreaker. I learned of this marque second-hand from a GM Tech Center automotive stylist. See it in a wind tunnel. They also built some wild-looking trucks. Very
steampunk before there was such a thing.
Standard axial-flow turbojet. So why are they calling it a "rocket car"? Rockets are completely different from jet engines.