Tarzan, who weighs 740 N, swings from a cliff at the end of a 29.0 m vine that h

Question

Tarzan, who weighs 740 N, swings from a cliff at the end of a 29.0 m vine that hangs from a high tree limb and initially makes an angle of 39.0 degree with the vertical. Assume that an x axis extends 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 575 N. (a) At the moment of takeoff, what is the force on Tarzan from the vine, in unit-vector form? F vector = N (b) At that moment, what is the net force on Tarzan, in unit-vector form? F_net vector = N (c) What is the net force on Tarzan, as a magnitude and angle relative to the positive direction of the x axis? magnitude N direction degree counterclockwise from the +x-axis (d) what is the acceleration of Tarzan, as a magnitude and direction, during takeoff? magnitude m/s^2 direction degree counterclockwise from the +x-axis

Explanation / Answer

(A) force from the vine is F = 740*sin(39) i + 740*cos(39)j

F = 465.71 i + 575 j

(B)net force= Fnet= F+ mg

Fnet = 465.71 i +575j-740j

Fnet=465.71i-165j

(C) magnitude of Fnet= sqrt(465.712+(-165)2) = 493.4 N

theta = atan(-165.1/465.71) =-19.51

required angle is 360-19.51 = 340.49 degrees counterclockwise from positive x axis

(d) mass of tarzan= 740/9.8=75.5 kg

magnitude of accelaration a = F/m = 493.4/75.5 =6.53 m/s2

direction of cceleration= theta=340.49 degrees counterclockwise from positive x axis

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