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That's why I suggested shooting him directly towards it, wouldn't he just keep going unless he somehow manages to hit something on the way there? Surely he'd end up hitting the sun?
He'd still have the 30 km per second (67,000 mph) of sideways velocity that Earth has when it's orbiting the sun, and that speed is enough to prevent Earth from ever hitting the sun.
Orbits aren't very intuitive; if you want something you launch from Earth to fall straight into the sun, you actually need to fire it directly opposite to the direction that Earth orbits in. So if you imagine Earth orbiting clockwise, you want to shoot the thing counterclockwise. If you do that at the right speed, you counteract all the orbital speed and the thing just falls into the sun.
If you can speed something up a completely unlimited amount then sure you could aim straight at the sun and just fire it so fast that it hits the sun anyway. It'll be off-centre a bit but the sun is pretty big. Consider how much of the sky isn't sun though. If the sun is directly overhead and you shoot straight at the sun, the thing you fired is already going 30 km/s sideways before you even started. We could do the trig to figure out how fast you need to shoot it to still hit the sun anyway but I think the more important part here is getting a feel for the motion involved.
How about if you leave the earth's atmosphere first, come to a stop, then fire him/accelerate directly at the sun? Or I guess just leave him there so he falls into it slowly? I'm not trying to be difficult or anything I'm just interested.
Depends on what you mean by the "come to a stop" bit. Stop relative to Earth? You're still going Earth speeds relative to the sun, which is what you're trying to hit. It's like throwing a ball at something while driving past it. If you mean stop relative to the sun then sure, you don't even need to shoot him towards the sun, he'll fall right in. The trouble is that stopping relative to the sun is specifically the bit that takes a lot of energy.
Cool, thanks for the info, it's very interesting. I, for one, vote for trying it with Musk, even if it goes wrong he won't be here anymore.
Even if we fail, Elon Musk ends up further away than he currently is