Final answer:
The student's error lies in the misunderstanding that gravitational potential energy depends on the object's absolute height, rather than the change in height relative to a reference level. The correct gravitational potential energy calculation involves the mass, gravity, and change in height.
Step-by-step explanation:
The mistake the student made in calculating the gravitational potential energy of a 1.0-kg rock falling from 100.0 m to 90.0 m is option C) The gravitational potential energy of an object depends on the object's height and not on the change in height. This statement is incorrect because the gravitational potential energy (GPE) of an object indeed depends on the change in height relative to a defined zero level. The correct formula for calculating the GPE of an object near Earth's surface is GPE = mgh, where m is the mass, g is the acceleration due to gravity, and h is the height above the chosen reference point.
To calculate the decrease in gravitational potential energy as the rock falls from 100.0 m to 90.0 m, the student should have used the difference in height (Δh = 10.0 m) in the calculation: ΔGPE = mgΔh. This would yield the correct change in GPE as the rock falls the specified distance.