1. The problem statement, all variables and given/known data A marble that is rolling without slipping approaches a hill at 8.5 m/s. How high vertically will the marble go under these circumstances: If the hill is rough enough to prevent any slipping? If the hill is perfectly smooth? Why does the marble rise to different heights when it had the same initial kinetic energy in both cases? 2. Relevant equations ME=KE+PE KE=1/2mv^2+mgh PE=mgh 3. The attempt at a solution KE(initial)=1/2(8.5)^2+9.8(0)=144.5 I have no idea how to solve for final or even if thats what to do next. PE(initial)=0 I'm not sure how to solve final without knowing the height for sure. Like, I said earlier I don't even know if this is the correct start to solve this.