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Answer to Question #28801 in Mechanics | Relativity for holly

Question #28801
Parents concerned about the safety of their children playing at a nearby lake have asked you to investigate. A tall tree with many large branches stands on the shore. The children have attached a rope to a branch 20 ft above the lake. The branch reaches out over the lake so that, when the rope hangs straight down, it just touches the lake. Children use this rope to swing from lower branches in the tree to the lake where they let go of the rope at its lowest point and go into the water. You watch as a child climbs 12 feet up the tree, grabs the taut rope 4.0 feet above its end, pushes off the tree, and swings over the water. You wonder if a child pushing off from the tree too fast could break the rope. First you test the rope and determine that it can safely hold 400 lbs. Next you determine that the heaviest child using the lake weighs 100 lbs. With that information you calculate the maximum safe distance from the bottom of the tree that the swinging child could enter the water.
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