To determine which station would have the lowest potential energy when throwing a rock up a mountain, it's important to understand the concept of gravitational potential energy (PE), which is given by the formula:
\[ PE = mgh \]
where:
- \( m \) is the mass of the rock,
- \( g \) is the acceleration due to gravity (approximately \( 9.81 , \text{m/s}^2 \) near the surface of the Earth),
- \( h \) is the height above a reference level (ground level, in this context).
The potential energy is lowest at the reference point. If we assume ground level is the reference point (where \( h = 0 \)), then any point above ground level (including any station up the mountain) will have a higher potential energy because \( h \) will be positive.
Thus, the station situated closest to the ground (or at the lowest elevation on the mountain) would have the lowest potential energy. Any station that is higher up the mountain will have a higher potential energy due to the positive value of \( h \).
In conclusion, the station at the lowest elevation (ground level or the starting point of the mountain) will have the lowest potential energy.