Centripetal Acceleration with Tarzan

[PeachBanana]

Homework Statement

Tarzan plans to cross a gorge by swinging in an arc from a hanging vine, as shown in the figure.
If his arms are capable of exerting a force of 1200 N on the vine, what is the maximum speed he can tolerate at the lowest point of his swing? His mass is 100 kg, and the vine is 4.5 m long.

Homework Equations

Tension force - mg = ma
(a * r)^1/2 = v

The Attempt at a Solution

1400 N = (100 kg)(a)+(100 kg)(9.8m/s^2)
420 N = 100kg * a
a = 4.20 m/s^2

(4.20 m/s^2)(2.25m)^1/2 = v

Why is it incorrect to use 2.25 m as the radius? They gave the entire length of the vine.

 

[BruceW]

If you look at the picture, what point is tarzan 'orbiting around' ?

 

[genericusrnme]

If you look at the picture, what point is tarzan 'orbiting around' ?

I lol'd

The picture reminds me of a picture on one of the exams I did a while back in high school, there's some bizarre half black half white basketball playing hybrid

Also, what BruceW said

 

[PeachBanana]

If you look at the picture, what point is tarzan 'orbiting around' ?

Oh I see. That's more clear. He's orbiting around the very top of the tree, not the middle of the vine.