Final answer:
The distance between the coaster and the Earth increases due to gravity as the roller coaster moves up the first hill, as this force is responsible for increasing the coaster's potential energy.
Step-by-step explanation:
As you move up to the first hill on a roller coaster, the distance between the coaster and the Earth increases primarily because of gravity. Neither centrifugal force, air resistance, nor magnetic force is responsible for increasing the distance between the roller coaster and the Earth during ascent. This can be understood in terms of energy, where the roller-coaster-Earth system's gravitational potential energy (APEg) increases as it moves away from Earth and is converted to kinetic energy (KE) as it moves downhill, provided work done by friction is negligible. If all APEg is converted to KE, this illustrates the conservation of mechanical energy principle.
In reference to the provided information, centrifugal force acts on a merry-go-round and is a fictitious force experienced in a rotating frame of reference. It is not the force that physically increases the distance during the initial ascent of a roller coaster but is instead a perceived force that passengers might feel while rotating with the merry-go-round or other amusement park rides like the spinning barrel. The actual force involved in uphill motion on a roller coaster is gravity, which initially does work against the roller coaster to increase its potential energy.