Question

Tarzan (m = 78.4 kg) tries to cross a river by swinging from a vine. The vine is 10 m
long. Tarzan doesn't know that the vine has a breaking strength of 1045 N. What
maximum speed (in m/s) can Tarzan have at the bottom of the swing (as he just clears
the water) in order to safely cross the river without breaking the vine?

PLEASE LEAVE FULL ANSWERS!
At the bottom of the swing, the vine is subject to two forces,
gravity force = mg
centripetal force = mv^sup2;/r
m=mass of Tarzan (kg)
g=acceleration due to gravity (9.81 m/s²)
v=tangential velocity (m/s)
r=radius of circular motion
=length of vine (m)

At point of rupture of the vine,
mg+mv²/r = 1045 N
Solve for v.

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