Question

Tarzan, who weighs 778 N, swings from a cliff at the end of a 15.8 m vine that hangs from a high tree limb and initially makes an angle of 23.6° with the vertical. Assume that an xaxis 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 713 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?

Answer 1

Given is:-

Weight of the Tarzan = 778N

Length of the vine = 15.8m

Initial angle = 23.6 degrees

Tension in the vine without Tarzan = 713N

Now,

Part-a

Force from the vine

Part-b

Net force acting on Tarzan is

Part-c

magnitude of the net force is

Part -d

direction is given by

below horizontal

Part-e

magnitude of accelerataion is F =ma

or

by plugging all the values we get

Part-f

direction of tarzan's acceleration is parallel to direction of force hence

Hence 23.58 degrees below horizontal