Final answer:
The climber's change in potential energy is 1,471,500 joules, and the work done during the climb is equal to the change in potential energy, assuming no other energy transfers, which is also 1,471,500 joules.
Step-by-step explanation:
The change in the climber's potential energy can be calculated using the formula for gravitational potential energy (PE = mgh), where m is the mass, g is the acceleration due to gravity (9.81 m/s2 on Earth), and h is the change in height. The climber's mass is 150 kg and the change in height (Δh) is 4,500 m - 3,500 m = 1,000 m. Therefore, the change in potential energy is PE = 150 kg * 9.81 m/s2 * 1,000 m = 1,471,500 joules (J). The work done by the climber to reach the higher altitude is equal to the change in potential energy, assuming there are no other energy transfers like kinetic energy or work against friction. So, the work done by the climber is also 1,471,500 J.