Problem #49 (ch. 12) doesn't seem to give enough information of solve the problem (I'm sure it actually does give enough info-- but I cant seem to see how to do it). It seems like it should involve integrating from the right side to the left bound, but there's not enough info to approximate the line under which we want to integrate. Am I thinking about this completely wrong?
Using conservation of energy, you can determine the total kinetic energy of the sphere when it 'launches' off of the horizontal section at the right-hand end of the track. You can then use something like equation 24a in Ch.12 to determine the (horizontal) speed of the center of mass at that moment -- after that it is a simple projectile problem. One additional note: you don't need to know the radius or the mass of the sphere, they will both eventually divide out of the problem.