Tarzan, who weighs 796 N, swings from a cliff at the end of a 24.1 m vine that h

Question

Tarzan, who weighs 796 N, swings from a cliff at the end of a 24.1 m vine that hangs from a high tree limb and initially makes an angle of 26.6 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 712 N. Just then, what are the force from the vine on Tarzan in unit-vector notation, and the net force acting on Tarzan in unit-vector notation? What are the magnitude and the direction (measured counterclockwise from the positive x-axis) of the net force acting on Tarzan? What are the magnitude and the direction of Tarzan's acceleration?

Explanation / Answer

immediately after tarzan steps off, following forces are acting on him:

tension acting along the vine

weight of tarzan, acting in downward direction

a) force exerted by vine=tension in the vine=712 N,along the vine

as given that the vine is making an angle 26.6 degree with vetical, tension will also make the same angle with vertical

hence component along x axis=712*sin(26.6)=318.8 N

component of force along y axis=712*cos(26.6)=636.64 N

in unit vecto notation, force exerted by the vine=318.8 i +636.64 j

b)
weight of tarzan=-796 j (as it is vertically downward)

then net force=tension + weight of tarzan

=318.8 i -159.36 j

c)magnitude of force=sqrt(318.8^2+159.36^2)=356.41 N

d)
angle with +ve x axis=arctan(-159.36/318.8)=-26.56 degrees

e)mass of tarzan=weight/g

=796/9.8=81.224 kg

then acceleration of tarzan =net force/mass

=3.925 i -1.962 j

magnitude of acceleration=sqrt(3.925^2+1.962^2)=4.3881 m/s^2

f)angle of acceleration with positive x axis=arctan(-1.962/3.925)=-26.56 degrees

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