This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.

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Answer
645 , \text{N}$ (given).
To solve these questions, I need the following information, which is not provided in the image:
Please provide these values so I can calculate the answers.
However, I can outline the formulas and steps you would use once you have the missing information:
Let:
(i) How much work does the climber do on the backpack? Work done () is calculated as the force applied multiplied by the distance moved in the direction of the force. In this case, the force is the weight of the backpack, and the distance is the height climbed.
(ii) If the climber weighs 645N, how much work does she do to lift herself and the backpack? The total force to be lifted is the sum of the climber's weight and the backpack's weight.
(iii) What is the average power developed by the climber? Average power () is the total work done divided by the time taken.
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To solve these questions, I need the following information, which is not provided in the image: The weight of the backpack.
This physics problem tests your understanding of fundamental physical laws and their applications. The step-by-step solution below breaks down the problem using relevant equations and physical reasoning.