- A jet engine,
- a rocket engine, and
- a conventional automotive internal combustion engine.
Now I'm thinking these guys are just geeking out because, well, someone gave them some money and said "build a really exotic car", and they just went nuts. I mean I can see having a jet or a rocket engine if you are going to attempt these kind of speeds, but why would you need both? And then I thought about it for a bit because they must have some kind of reason for doing this. I mean nobody puts up that much money ($10 million, more or less) just so some guys can geek out. Okay, nobody besides the military anyway. This is what I came up with.
They want to go 1,000 Miles Per Hour. You aren't going to do that with a wheel driven machine, too many problems with traction and the drive train, so you need a jet or a rocket. Pound for pound, rockets are much more powerful than jet engines, so I figure they are going to use the jet to get somewhere around the speed of sound and then kick in the rocket to get the last few hundred MPH. The rocket engine is a hybrid, which means it uses a solid fuel and a liquid oxidizer. The benefits here are that you only need one pump for the oxidizer, (conventional liquid fuel rockets have two pumps) and you can turn it off, which could be important if things go haywire. Conventional solid fuel rockets can't be turned off. They burn until they burn out. Pretty much unstoppable.
The third engine, the automobile engine is used only to drive the oxidizer pump for the rocket engine. Rockets consume a great deal of fuel very quickly, and when you are pumping fuel into the combustion chamber you need to overcome the pressure of the combustion that is trying to force it's way out. The only reason you can succeed in this endeavor is that the volume you are forcing in is very small compared to the volume of gas that is trying to escape. Regular rocket engines using turbines to drive the pumps, but turbine engines are very expensive. They are also very light weight and weight isn't so important for this project, so a conventional, relatively inexpensive engine is the ticket here.
The reason they are using a jet for the initial acceleration is that rockets consume a great deal of fuel, so by using a jet they are able to reduce the size of the rocket engine and it's associated fuel tank.
That leaves the question of why they are using a rocket at all. I mean jet fighter aircraft routinely reach speeds well in excess of 1,000 MPH, so why not just use the jet engine and dispense with the rocket? I can think of two possible reasons for this. One is aerodynamics. Jet aircraft are operating far from the ground. Being this close to the ground and trying to go this fast could be problematic. The other is that in order to get the thrust they need, they might need an afterburner, and afterburners are big and inefficient. Including an afterburner would probably double the length of the car. Take that and combine it with additional jet fuel you would need to carry and it might be that a rocket engine is more efficient.