Ropes/Pulleys with moving weights

[Feodalherren]

Homework Statement

Find the velocity of block B (the one to the right) A has a mass of 3kg and B a mass of 5kg. Pulleys and rope are ideal.

Homework Equations

F=ma

The Attempt at a Solution

I used two different methods, got the same WRONG answer. The correct answer is Vb= -35.8m/s
Let me know if you can't see what the pictures say

 

[Nathanael]

How is it consistent for T=49.1 N but 2T=29.43 N if it's the same rope? Tension doesn't vary across an ideal rope, because the rope is massless.

You can't say the tensions are equal to the weights. The objects will accelerate; but if the tension equals the weight, how would the objects accelerate?
I would leave the tension unknown and eliminate it, no reason to solve for it.

 

[Feodalherren]

I used this method:

 

[Nathanael]

Ah, I didn't see that you wrote "static analysis" above that part.

In either eq 2 or eq 3, you have an extra factor of -1 on the acceleration term.

Edit:
Actually, it could be fixed by slightly altering any of your 3 equations; they just need to be consistent.
You said, -a_b = 2a_a which implies that you're letting a_b and a_a represent the magnitudes and direction (one of them is negative) of acceleration; but then you have an extra factor of -1 on a₃ in eq.3, which implies that you're taking a_a and a_b to be just the magnitude