A large quarter pipe block of mass M is frictionless and unfixed, so it can slide, is initially at rest on the floor. Quarter pipes have a circular surface of radius R as shown below. A skateboarder on a frictionless board (wearing frictionful shoes), altogether of mass m < M, approaches the pipe with speed vo.

(a) What is the maximum height h above the floor that is reached by the skater? Assume vo is small enough so that h < R. Express your answer using some or all of the following variables: vo, g, m and M.

(b) After the skater reaches the maximum height, he slides back down the pipe. After the two separate, what is the speed of the skater and the pipe? Express your answer using some or all of the following variables: vo, g, m and M.

R m M