Final answer:
Using the formula GPE = mgh, the rock climber's mass is calculated to be 58.8 kg when her gravitational potential energy (117,600 J) and height above the ground (200 m) are known.
Step-by-step explanation:
The question relates to gravitational potential energy (GPE) and the formula to calculate the mass of an object when the height and GPE are known. To solve for the rock climber's mass, we use the formula GPE = mgh, where GPE is the gravitational potential energy in joules, m is the mass in kilograms, g is the acceleration due to gravity (approximately 10 m/s² on the Earth's surface), and h is the height in meters. Plugging in the values, we have 117,600 J = m * 10 m/s² * 200 m. To find the mass m, we can rearrange the formula to m = GPE / (gh).
Solving for m:
m = 117,600 J / (10 m/s² * 200 m) = 117,600 J / 2000 m²/s² = 58.8 kg.
Therefore, the rock climber's mass is 58.8 kg.