Final answer:
A skater can reach the same maximum height on both sides of a ramp due to the conservation of energy in an ideal frictionless situation. However, a roller coaster's second hill is shorter than the first due to energy losses primarily from friction and air resistance, which decrease the total energy available to be converted back into potential energy.
Step-by-step explanation:
The phenomenon in question involves concepts of conservation of energy and frictionless motion. Both the skater and the roller coaster operate under these principles. A skater on a ramp can achieve the same maximum height on both sides if there is no loss of energy due to friction or air resistance, because the potential energy at the top of one side will be converted entirely into kinetic energy at the bottom, and then back into potential energy on the other side. The conservation of energy ensures that the skater reaches the same height.
However, the second hill of a roller coaster must be less tall than the first because there are energy losses mostly due to friction and air resistance. The roller coaster does not maintain all the potential energy it had at the start; some is converted to heat and sound, resulting in less energy to convert back into potential energy after the first descent, hence the second hill is shorter.