Another application of Newton's laws?

Question

Tarzan, who weighs 820 N, swings from a cliff at the end of a 20 m vine that hangs from a high tree limb and initially makes an angle of 22 degrees with the vertical. assume than an x axis extends horizontally away from the edge of the cliff and the y axis extends upward. Immediately after Tarzan steps off the cliff the tension in the vine is 760 N. Just then, what are (a) the force on him from the vine in unit vector notation and the net force on him (b) in unit-vector notation and as (c) a magnitude and (d) an angle relative to the positive direction of the x axis? What are the (e) magnitude and (f) angle of Tarzan's acclereation just then.

I'm completely lost on what to do.

Answer 1

Assuming that the vine hangs from a point beyond the cliff, otherwise Tarzan wouldn't go anywhere; he'd just have to hang out with Jane.
theta=22 deg
fx = 760*sin(theta)
fy = 760*cos(theta)
(a) f = 760*[fx,fy]
w=820; m = w/g
define fn=net force
fnx = fx
fny = fy-w
(c) mag(fn) = sqrt(fnx^2+fny^2)
(d) angle(fn) = arctan(fy/fx)
unit(fn) = [fnx/mag(fn),fny/mag(fn)]
(b) fn = mag(fn)*unit(fn)
(e) mag(a) = mag(fn)/m
(f) angle(a) = angle(fn)
Note that tension 760 = 820*cos(22 deg). Thus the equations above could be expressed purely in terms of w by substituting w*cos(theta) for 760.