Here's a problem that my teacher specifically assigned to me to make it as hard as possible.
A ball with a radius of 1 is dropped into a parabolic container whose surface is described by rotating y=x^2 around the y-axis. When the ball comes to rest, how far is its bottom from the bottom of the container?
(The image above isn't the exact image that's on the problem, but it's an accurate re-creation.)
The image above is missing point a (which is at the center of the circle and on the y-axis. The slanted line going from point a (the center) to the point labeled (x,y) = 1 because it's a radius.
Okay, so I'm not 100% sure how to start this problem. Is it even possible to get an exact value, or will I have to find the distance between the two bottoms in terms of x?