Question 01/00

CLIMBING AN ICEBERG

A mountaineer climbs an iceberg - icy cone-shaped mountain. He has made a loop with non-sliding knot and thrown it over the top of the mountain as shown in the figure. If the mountain is steep enough, the climber will reach the summit; if it is not, the loop will slip of the top. Find the critical slope of the mountain.

D. Khmelnitskii told us this problem. He heard it from M. Spector in 1970. [5/2001: See also a postscript in the answer.]

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