Physics In the Playground

[noparlpf]

That depends. Do we have to account for air resistance?

If yes, then you'll never actually reach the other side, as quite a bit of your kinetic and gravitational energy will be lost along the way.

If no, then I remember solving that in class once, and I think the answer was somewhere around half an hour. I also remember that, provided friction is assumed to be 0 the whole way, it doesn't actually matter whether the tunnel goes through the center or not. A tunnel going only a quarter of the way around the world (or any other fraction, even traveling 1 inch to the side) would have the same transit time, provided only that it is straight and powered only by gravity.

I assumed air resistance would stop you from getting there, and that eventually you'd fall back and sort of oscillate around the center of the earth for a while until you starved. So without air resistance (so you have to have a suit or something?) how many gees does the faller experience at most?

I haven't done any math for this one, but I expect the cup would lose heat to its surroundings faster than any gained from your yelling. So, take your pick between "forever", "undefined", and "no answer".

That's what I said. Okay, cool.

The biggest problem is, that once you go deep enough the air would turn liquid because of the pressure.

I think we're pretending there's no air, because otherwise the answer is "you'll never get there".