physics

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The hero pursues the villain up to the top of a bungee jumping apparatus. The villain appears trapped but to create a diversion she drops a bottle. The hero quickly straps on the bungee cord to his leg and dives straight down to grab the bottle while its still in the air. Determine the length of the unstretched bungee cord. The hero is supposed to grab the bottle before the bungee begins to stretch so that the stretching of the bungee cord will stop him gently. You estimate that the hero can jump off the bungee tower with a maximum velocity of 10 ft/s straight down by pushing off with his feet and can react to the villains dropping the bottle by strapping on the bungee cord and jumping in 2 seconds.

Find the length of the un-stretched bungee cord.

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