Tarzan, who weighs 860 N, swings from a cliff at the end of a 22.7 m vine that h
ID: 1421796 • Letter: T
Question
Tarzan, who weighs 860 N, swings from a cliff at the end of a 22.7 m vine that hangs from a high tree limb and initially makes an angle of 22.0° 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 797 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
a)
Let i and j be unit vector along x and y axis
force on tarzan by vine = tension in vine = 797 N
It acts at an angle of 22 degree from vertical
F = 797*sin 22 i + 797*cos 22 j
= (298.6 i + 739 j) N
b)
W acts downward :
W = - 860 j
Net force = F + W
= 298.6 i + 739 j - 860 j
= (298.6 i - 121 j) N
c)
magnitude = sqrt (298.6^2 + 121^2 ) = 322.2 N
d)
direction = 360 - atan (121/298.6)
= 360 - 22.1
= 337.9 degree
Only 4 parts at a time
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