Difficult Centripetal Motion Problem

[Arooj]

Homework Statement

Tarzan swings from a vine 20 m long which makes an angle of 30° with the vertical. If he pushes off with a speed of 2 m/s, what is the tension in the vine at the lowest point of the swing? Tarzan has a mass of 80 kg.

Homework Equations

centripetal accelaration force = F
m = mass
r = radius of circle
v = tangential speed
F=m(v^2)/r

1/2mv^2 + mgh = 1/2mv^2 (I'm not sure about this, though)

The Attempt at a Solution

F = 80 (2^2)/ 20
F = 16 N

I don't know how to integrate the angle measure into the problem.

 

[Delphi51]

The 1/2mv^2 + mgh = 1/2mv^2 looks good. Use it to find the velocity at the lowest point. Then use Fc=m(v^2)/r with that value for v. Another force will add to this to make the total tension.