Tarzan, who weighs 900N, swings from a cliff at the end of a 40.0 m vine that ha

Question

Tarzan, who weighs 900N, swings from a cliff at the end of a 40.0 m vine that hangs from a high tree limb and initially makes an angle of 60.0 degrees with the HORIZONTAL. Assume that an x-axis extends horizontally away from the cliff edge and a y-axis extends upward. Immediately after Tarzan steps off the cliff, the magnitude of the total (net) force on the Tarzan is 451N. Assume, the maximum allowed tension on the vine is 770N and Tarzan is intact after he steps off the cliff a.) What is the magnitude of the tension on the vine. b.) What is the angle of the net force relative to the positive x-direction? c.) What is the magnitude of Tarzan's acceleration?

Explanation / Answer

The force components from the vine are 770cos60 = 385N up and 770sin60 = 666.8 N away from cliff: F(vine) = 666.8 i + 385 j The additional weight of 900 N down makes F(tot) = 666.8 i - 515 j. Or, F(tot) = 842.5 N at an angle of 37.6 degrees below horizontal Tarzan's acceleration is F/m = 842.5 /(900/9.8) = 9.17 m/s^2 at the angle -37.6 deg.

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