Final answer:
The hiker's potential energy at different huts is calculated using the formula PE = mgh. The potential energy is relative to sea level, and the loss or gain of potential energy can be found by subtracting the values at different altitudes.
Step-by-step explanation:
Potential Energy of a Hiker
a. The potential energy of the hiker at the first hut, which is 800 m above sea level, can be calculated using the formula PE = mgh, where m is the mass of the hiker, g is the acceleration due to gravity (approximately 9.8 m/s2), and h is the height above the reference point, which in this case is sea level. The hiker's potential energy at the first hut is:
PE = 70 kg * 9.8 m/s2 * 800 m
b. To determine the potential energy lost during the second day when the hiker moves to the second overnight hut at 500 m above sea level, we calculate the potential energy at both altitudes and find the difference. The potential energy loss is:
PE lost = PE at first hut - PE at second hut
c. The potential energy the hiker had when she started her journey at 200 m above sea level can be calculated similarly. It's important to note that the potential energy at the starting point serves as the baseline for calculating changes in potential energy during the hike.
d. Potential energy of the hiker back at her original starting position is relative to the reference point; hence, she would have the same potential energy as calculated in part c as she returns to the same altitude.