Final answer:
The potential energy of the hiker increases as she hikes up a mountain.
Step-by-step explanation:
The potential energy of an object is given by the equation PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height above the reference level. In this case, the hiker starts at sea level and hikes up 30 feet, so the change in height is 30 feet. Since the hiker is not returning to the starting point, we don't need to consider the rest and the second climb.
To calculate the potential energy at the highest point, we can use the equation PE = mgh. The mass of the hiker is not given, so we cannot calculate the exact potential energy. However, we can determine that the potential energy is higher than when the hiker started because the hiker has climbed up.