Tarzan, who weighs 791 N, swings from a cliff at the end of a 17.7 m vine that h
ID: 1421898 • Letter: T
Question
Tarzan, who weighs 791 N, swings from a cliff at the end of a 17.7 m vine that hangs from a high tree limb and initially makes an angle of 18.0° 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 752 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
=18.0 deg
T=752 N
L=17.7m
W= 791N
a) FTvx=Tx= 752cos18 = 232.4 N
FTvy= Ty= 752cos18 = 715.2 N
The force from the vine on Tarzan , FTv = (232.4 i + 715.2 j) N
b) FTx = Tx= 752cos18 = 232.4 N
FTy = Ty - mg= 752cos18 -791 = 715.2 -791 = -75.8 N
FT = (232.4 i - 75.8 j)
c) FT = sqrt(232.4^2 + 75.8^2) = 244.45 N
d) FT= tan^-1(75.8/232.4) = -18.0 deg = 180+18 = 198 deg counterclockwise from
+X acis.
e) aT = FT/m=244.45/(791/9.8) = 3.03 m/s^2
f) aT is same as FT , thus = aT =198.0 deg
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