Tarzan, who weighs 860 N, swings from a cliff at the end of a 21.8 m vine that h

Question

Tarzan, who weighs 860 N, swings from a cliff at the end of a 21.8 m vine that hangs from a high tree limb and initially makes an angle of 26.6° with the vertical. Assume that an x axis points horizontally away from the cliff edge and a y axis extends upward. Immediately after Tarzan steps off the cliff, the tension in the vine is 769 N. Just then, what are (a) the force from the vine on Tarzan in unit-vector notation, and (b) the net force acting on Tarzan in unit-vector notation? What are (c) the magnitude and (d) the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are (e) the magnitude and (f) the direction of Tarzan's acceleration just then?

Explanation / Answer

The force components from the vine are 769cos26.6 = 687.60 N up
and 769sin34 = 344.3 N away from cliff: F(vine) = 344.3 i + 687.60 j

The additional weight of 860 N down makes F(tot) = 344.3 i - 172.4 j

Or, F(tot) = 385.05 N at an angle of 26.6 degrees below horizontal

Tarzan's acceleration is F/m = 385.05/(860/9.8) = 4.39 m/s^2 at the angle -26.6 deg.

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