Answer :

Final answer:

The minimum diameter of manila rope used for lifelines is 3/4 inch, as per safety standards. The given data relates to the stretch of a nylon climbing rope under the weight of a mountain climber, which is different in context to the lifeline question.

Explanation:

The question at hand involves the strength and stretch characteristics of a manila rope used for lifelines; however, the information provided pertains to a nylon climbing rope used by a mountain climber. These nuances are important when answering the original question on minimum diameter of manila rope used for lifelines. In the context of safety standards for lifelines made out of manila rope, the Occupational Safety and Health Administration (OSHA) specifies that the minimum diameter should be 3/4 inch for lifelines. Therefore, the correct answer to the student's question is option 2) 3/4 inch.

Regarding the provided data, it corresponds to a scenario where a 65.0-kg mountain climber stretches a 0.800-cm diameter nylon rope when hanging 35.0 m below a rock outcropping, resulting in a stretch of 9 cm. This scenario illustrates the mechanical properties of nylon rope, specifically, its tensile strength and elasticity under a given weight. The question about the rope being a bungee cord is a separate consideration, as bungee cords are designed to stretch significantly more than climbing ropes.

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