Walking by a pond, you find a rope attached to a stout

Chapter , Problem 57

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Walking by a pond, you find a rope attached to a stout tree limb that is above ground level. You decide to use the rope to swing out over the pond. The rope is a bit frayed, but supports your weight. You estimate that the rope might break if the tension is greater than your weight. You grab the rope at a point from the limb and move back to swing out over the pond. (Model yourself as a point particle attached to the rope from the limb.) (a) What is the maximum safe initial angle between the rope and the vertical at which it will not break during the swing? (b) If you begin at this maximum angle, and the surface of the pond is below the level of the ground, with what speed will you enter the water if you let go of the rope when the rope is vertical?