Joe and Sal are in a rollerbladers' club that is building a ramp to reach ne w levels of extremeness. The ramp is to be a simple incline, so that after coasting horizontally, a skater will ride up the slope at some angle θ. Sal suggests making the slope as steep as possible to maximize the height that will be reached. Joe whips out a pencil and paper to prove to Sal that, if the surfaces are smooth, the height reached is independent of the angle of the slope. Sal acknowledges that even though Joe is being smug and obnoxious, his argument is sound. Show Joe's proof.