In the popular television show Man Versus Wild, Bear Grylls attempts to survive

Question

In the popular television show Man Versus Wild, Bear Grylls attempts to survive in remote areas. In one recent episode ("Georgian Republic"), Bear must cross a fast-flowing river. Strung across the river is an old rope* with considerable sag. Bear's idea is to hitch a pully/harness to the rope and slide across the river.As a stunt coordinator with a background in physics, you have been asked to determine whether Bear can make it across the river and whether the rope will hold his weight. Bear is rather small, with a mass of only about 46.9 kg, including his equipment. The crossing distance is roughly W = 13.1 m and the rope is tied H = 2.62 m lower on the opposing the bank. Judging by the sag in the rope, its length is about 17.1 m. Calculate the tension in the rope once Bear reaches a point of equilibrium. Assume the rope does not stretch.If Bear can make it far enough across (at least 9.7 m from where he starts), he can drop down onto the river bank below. How far will he travel across?

Explanation / Answer

tan x=2.62/17.1=0.153216374

x=8.712 degrees

T*sin x= m*g

T=46.9*9.8/sin 8.712

T=3034.4

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