A mountain climber wishes to climb up a frictionless conical mountain. He wants to do this by throwing a lasso (a rope with a loop) over the top and climbing up along the rope. Assume that the climber is of negligible height, so that the rope lies along the mountain, as shown in Fig. At the bottom of the mountain are two stores. One sells ?ocheap?? lassos (made of a segment of rope tied to a loop of fixed length). The other sells ?odeluxe?? lassos (made of one piece of rope with a loop of variable length; the loops length may change without any friction of the rope with itself). See Fig. When viewed from the side, the conical mountain has an angle a at its peak. For what angles a can the climber climb up along the mountain if he uses?(a) A cheap?? lasso?(b) A deluxe?? lasso?
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