Mixing new and old is pretty cool. The catapult itself would not need solar energy to work, but I’m guessing your idea is that you will be able to drive the catapult, right?
To put the catapult on the carframe, (No chassi) of, for example an old vw beetle (engine in the back), or some other small car would be a good idea. I think the effect of a massive catapult on a small vehicle would be sweet.
It would be pretty cool if you made some sort of robotic arm to pick up stones and other ‘throwable’ items to put in the catapult. That way you would never run out of ammo as long as there were stuff lying around.
Nice concept, and environment friendly.