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Tarzan wights 820N, swings from a cliff at the end of a 20m vine that hangs from a high tree limb and initially makes an angle of 22 degrees with the vertical. Immediately after Tarzan steps off the cliff the tension in the cine is 760N. Choose a coordinate system for which the x axis points horizontally away form the edge of the cliff and the y axis points up. a)What is the magnitude and dicection of the net force acting on Tarzan? b) What is the magnitde and direction of his acceleration?

What would be the equations I should use to solve the problems? I can't find them from my textbook. a) is expose to be 307 N at -22 degrees from the positive x axis. b) is 3.67 m/s^2 at -22 degrees from the postitive x axis.

(a) Two forces act on Tarzan as he leaves the edge of the cliff; the rope tension (at a 22 degree angle to vertical) and gravity (820 N down). They already tell you what the vine tension is, so you just have to "resolve" that into
760 N sin 22 = 284.7 N horizontal and
760 N cos 22 = 704.7 N vertical. The net downward force is
820 - 704.7 = 115.3 N and the net horizontal force is 284.7.
Take the resultant of those for the magnitude of the net force. The ratio of the two forces equals the tangent of the direction angle.

(b) Divide each of those forces by his mass (820 N/9.8 m/s^2 = 83.7 kg) to get the accelerations in the corresponding directions

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