Final answer:
In a balloon above a roller coaster, only horizontal movement could be observed. Galileo's principles and relative motion illustrate why people in different frames of reference perceive motion differently. In amusement rides, centrifugal forces and friction act on riders to provide the sensations they feel.
Step-by-step explanation:
Understanding Motion and Forces in Amusement Park Rides:
If you were in a balloon above the roller coaster and could only see horizontal movement, you would observe the coaster cars moving along the track parallel to the ground without being able to discern any of the vertical drops or climbs. This scenario calls to mind the principles discussed by Galileo concerning relative motion. Similarly, when observing a train from a platform, you would see it moving past you, while a passenger on the train would see you as stationary (Option A from GRASP CHECK). This is because the motion is relative to your frame of reference.
In a parallel universe where ocean waves are longitudinal, a surfer would move forward and backward horizontally with no vertical motion (Option B from GRASP CHECK).
Addressing the misconception about Earth's motion in the heliocentric theory, it is suggested that if Earth were moving, we might not necessarily feel the motion, as our experiences with moving trains, buses, or ships can show — sometimes we can't tell who is moving without additional cues.
Regarding the amusement park ride where riders feel pinned to the wall of a spinning barrel, in an inertial frame of reference, this is because of centrifugal force and friction. The real forces acting on them are the normal force exerted by the wall and the friction that prevents them from sliding down.
When discussing forces acting at a distance, like gravity, the ultimate determinant of truth in physics is empirical evidence and consistent experimental results, which led to widespread acceptance of such concepts in physics.