Tarzan, who weighs 792 N, swings from a cliff at the end of a 17.1 m vine that h

Question

Tarzan, who weighs 792 N, swings from a cliff at the end of a 17.1 m vine that hangs from a high tree limb and initially makes an angle of 26.1 degree 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 711 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? (a) Number i + j Units (b) Number i + j Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units

Explanation / Answer

a) T = 711 sin 26.1 degree i + 711 cos 26.1 degree j N

= 312.8 i + 638.5 j N

b) F = 312.8 i + 638.5 j - 792 j

= 312.8 i -153.5 j N

c) F = sqrt(312.8^2 + 153.5^2)

= 348.4 N

d) direction = 360 degree - arccos (312.8/348.4)

= 333.9 degree

e) a = F/m = 348.4/(792/9.8) = 4.31 m/s^2

f) direction = 360 degree - arccos (312.8/348.4)

= 333.9 degree

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