Hey pat, the process you've described for the solution is correct and I just solved it to get R(Vo)^2/(2gR-Vo^2) After integrating, (P.E)at H = mgR^2 [ (1/R) - (1/(R+H)) ] <--- Did you get this? Equating (P.E)at H with (K.E.)initial, you get the desired answer. I think you did the integral wrong, or did some algebra mistake while equating. Possible mistake; integral(1/(R+r)^2, r) <--- did you change variable here and forget to change the limits of integration.