Tarzan, who weighs 730 N, swings from a cliff at the end of a 12.0 m vine that h

Question

Tarzan, who weighs 730 N, swings from a cliff at the end of a 12.0 m vine that hangs from a high tree limb and initially makes an angle of 32.0° 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 619 N.

(a) At the moment of takeoff, what is the force on Tarzan from the vine, in unit-vector form?

(b) At that moment, what is the net force on Tarzan, in unit-vector form?

(c) What is the net force on Tarzan, as a magnitude and angle relative to the positive direction of the x-axis?

(d) What is the acceleration of Tarzan, as a magnitude and direction, during takeoff?

Explanation / Answer

a)

here

Tx = 619sin32 = 328 i N

Ty = 619cos32 = 524.9 j N

b)

F = T - m*g

F = [328 i + (524.9 - 730) j] N = [328 i - 205.1 j] N

c)

then the magnitude is

F = sqrt(328^2 + 205.1^2)

F = 386.8 N

then the direction is

theta = tan^-1(-205.1/328) = -32.02deg = 327.98 deg

d)

a = F / m

a = 386.8 / (730/9.8)

a = 5.19 m/s^2

the direction is same as force

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