Is My Monkey Physics Calculation Correct?

[Apple123]

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A 5.0 kilogram monkey hangs initially at rest from two vines, A and B. Each vine is 10 meters in length with negligible mass.

Vine A is on the left with an angle of 30 degrees from the horizontal from the monkey and B is at 60 degrees from the horizontal of the angle next to the monkey.

1. Determine the tension of B while it is at rest
2. Determine the speed of the monkey.
3. Determine the tension of vine B at the lowest point through the swing.

Here is what i got:
1. T=Wcos(theta)
=(5)(9.81)(cos 60)
=24.525N

2. PE(i)=KE(f)
mgh=.5(m)(v^2)
(5)(9.81)(10-10sin60)=(.5)(5)(v^2)
v=5.127

3. T=mg+F(centripital)
=(5)(9.81)+((5*5.127^2)/10m)
=62.192 N

Can anybody confirm this for me? I have been stuck on this problem for like 2 hours, I am confused if i calculated the tension in part 1 right or if i accidentlly did the tension for vine A instead. This is my worst part of physics, so any help would be appreciated!

I see that the angles are compliments, so if i mess up on sine and cosine usage i will get the tension for the opposite vine. Thats why i don't know if I am doing this right.

 

[Fermat]

Does the first attachment looks like the arrangement of what is happening ?
http://img483.imageshack.us/img483/1479/apple1gj.th.jpg
The monkey is being supported by two vines. So both vines have a component in the vertical direction supporting the weight of the monkey.
To solve part a), you have to resolve the tensions in the vines into both horizontal and vertical forces. Then do a balance of forces with them, viz.

$$\Sigma F_V = 0$$
$$\Sigma F_H = 0$$

Should end up with two eqns in two unknowns, T_A and T_B.

I see that the angles are compliments, so if i mess up on sine and cosine usage i will get the tension for the opposite vine. Thats why i don't know if I am doing this right.

Do you have a problem determing whether to use sine or cosine ?
I use the definition of sine and cosine to help me figure it out. Perhaps the attachment2 will help.
http://img483.imageshack.us/img483/779/apple28za.th.jpg

About part b). How does the monkey move ?
Does it leap off a branch so many metres above its lowest point ?
?

 

[quicknote]

I can confirm that your calculations for the tension of vine B while at rest and the speed of the monkey are correct. However, for the tension of vine B at the lowest point through the swing, it is important to note that the tension will be at its maximum when the monkey is at the lowest point. Therefore, the equation should be T=mg+F(centripetal) = (5)(9.81) + (5*5.127^2)/10 = 67.192 N. This is because at the lowest point, the centripetal force is at its maximum, which is equal to the weight of the monkey. So the tension will be equal to the weight plus the centripetal force. I hope this helps clarify any confusion.