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Largest mass Tarzan can have and swing safely across the river

Tarzan tries to cross a river by swinging from one bank to the other on a vine that is 10.0 m long. His speed at the bottom of the swing, just as he clears the surface of the river, is 8.0 m/s. Tarzan does not know that the vine has a breaking strength of 1.0 x 10^3 N. What is the largest mass Tarzan can have and make it safely across the river?

Please show the work, answer and the formulas you used.

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Solution: Assume that the largest mass Tarzan can have is M (kg). Denote the length of the vine by R, so ...

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With good explanation and calculations, the problem is solved.