1. The problem statement, all variables and given/known data A boy is initially seated on the top of a hemispherical ice mound of radius r=13.8m. He begins to slide down the ice, with an initial speed vi=3m/sec. Approximate the ice as being frictionless. At what height does the boy lose contact with the ice? 2. Relevant equations 3. The attempt at a solution My instructor gave the hint that it has to do with how force is relevant to centripetal force. I first attempted finding the boy's direction and speed right as he started sliding off the ice by doing vector addition with the initial velocity (which I interpret as his speed in the x direction) and the centripetal acceleration ( interpreted as his speed in the y direction). I found the centripetal acceleration to be v2/r = (3)2/13.8 = 0.652m/s2. Then I found the initial angle θ=12.26°. I kind of abandoned that since I didn't think I was approaching it the right way at all. Going off of my instructor's hint, I figured the boy has to start off with a centripetal force, since his acceleration is centripetal to start with, then since he's not attached to the sphere his acceleration become free-fall. I'm not sure how I should go about calculating at what point his acceleration stops begin centripetal. I'm thinking I have to determine when that happens then use s=rθ to find the arc length, since I'm not sure how else to determine distance on the sphere.