A 85 kg rock climber first climbs 50 m up to the top of a quarry, then descends 75 m from the top to the bottom of the quarry. If the initial height is the reference level, find the potential energy of the system (the climber plus Earth) when the climber is at the top. Find the potential energy of the system when the climber is at the bottom.

To find the potential energy of the system, we can use the formula:

Potential Energy = mass * gravity * height

Given:
Mass of the rock climber (m) = 85 kg
Gravity (g) = 9.8 m/s^2 (acceleration due to gravity)
Height at the top of the quarry (h1) = 50 m
Height at the bottom of the quarry (h2) = 75 m

1. Potential energy at the top of the quarry (PE1):
Potential Energy (PE1) = mass * gravity * height

Substituting the given values:
PE1 = 85 kg * 9.8 m/s^2 * 50 m

Calculating:
PE1 = 41,730 Joules

The potential energy of the system when the climber is at the top of the quarry is 41,730 Joules.

2. Potential energy at the bottom of the quarry (PE2):
Potential Energy (PE2) = mass * gravity * height

Substituting the given values:
PE2 = 85 kg * 9.8 m/s^2 * 75 m

Calculating:
PE2 = 61,725 Joules

The potential energy of the system when the climber is at the bottom of the quarry is 61,725 Joules.