Jack & Jill

Jack and Jill went up the hill. They stayed and rested for a while and then came back home. This applet shows - how far from home along the path they were at any time: - how high above their home they were at any time: - how high above their home they were at any point along the path: Given any one of these curves - can you make the other two? Why or why not? Given any two of these curves - can you make the third? Why or why not?