The G’s from one of those slingshot rides are bad enough! I can’t even fathom 10,000x. I’m no expert but I’d imagine that would crush a car pretty quick.
Satellites need a specific velocity to maintain the orbit they are in. This speed is high enough that satellites burn up when they contact the upper atmosphere. In this case the slingshot velocity would need to be much greater than the orbital velocity to account for atmospheric drag and the change in potential energy between the Earth’s surface and the orbital height. That higher velocity would be at the dense part of the atmoshere right at the Earth’s surface. Preventing it from melting in the first 100,000 feet would be a big challenge.