1. The problem statement, all variables and given/known data We are trying to solve a problem where, we'll call him John, is being pushed down the hill too fast by Mary and when he goes back up the next hill he ends up flying up off the ground. We are trying to solve where, on the graph (coordinates) he lands. Here is what I know about the problem. He starts at the origin. Mary is pushing him at a velocity of 5 m/s. He starts at a standstill. Friction is to be ignored. His mass is only 1 kg and the sled is to be considered mass-less. Apparently for simplicity's sake? It's on earth so gravity is of course 9.81 m/s squared. 2. Relevant equations Equation of the hill is y(t)= -sin(x(t)). 3. The attempt at a solution I'm kind of lost, and I don't pretend to know much about math and physics, but this problem has piqued my interest and I'd like to know how to solve it. Thanks!