A skateboarder is skating through a half-pipe with a radius of 4 m. Initially she is in a crouched position with her center of mass 0.5 m above the surface of the half-pipe. She starts from rest with her center of mass a height of 3 m above the base of the half-pipe and experiences no loss of energy from friction as she moves. At the bottom of the half-pipe she stands up and lifts her arms into the air, thereby raising her center of mass to 1.0 m. She then continues up the other side of the half-pipe. What is the maximum height (in m) that her center of mass reaches on the other side of the half-pipe? You may model the skateboarder as a point particle.