Ropes and Pulleys - Really unintuitive answer I usually don't want to do this, but please go to this link, the solution is too big to post it here
http://engineering.union.edu/~curreyj/MER-201_files/Exam2_2_26_09_Solution.pdf 
And go to page 5 of the pdf. 
Briefly, the problem say

Determine the velocity of the 60-lb block A if the
  two blocks are released from rest and the 40-lb block B
  moves 2 ft up the incline. The coefficient of kinetic friction
  between both blocks and the inclined planes is $\mu_k$ = 0.10.

Things I am confused with the solution
1.First of all, I seriously thought lb was mass not force. after some googling, it turns out they are used interchangeably...
2.Where did they even get $2s_a + s_b = 0$ from? Why did they determine the change in distance this way? My first assumption was that if block B moved up 2ft, then block A should move down 2ft (the rope must "move" 2ft too right?). Then I wasn't sure, so I did a few triangles and found that the angle made a difference
3.Where did $2v_A = -v_B$ come from?
4 The FBD for block A is confusing, why is the friction force $F_A$ in the direction of the ropes? I thought it was block B that is going down? Am I the only one who had trouble deducting that the pulley and block A are the same object? 
5.Look at the final answer, how could $v_b$ be negative? The problem says block B goes UP.
If you are wondering, this is not homework. I am just interested in this problem and it is out of curiosity and very confused with the concepts. 
I've had at most introductory physics experience, but I think I should have been able to solve this still.
Thank you for reading
 A: 2 - the block 'A' is on a pulley, when it moves 1 ft the rope moves 2ft.  It has a 2:1 mechanical advantage, normally you would use this to move block 'A' half the distance you pull the rope and with twice the force - the point of a pulley is to use a smaller force for a longer distance.    
A: "2.Where did they even get 2sa+sb=0 from?"
From the assumption that the length of the rope does not change.
"Why did they determine the change in distance this way? My first assumption was that if block B moved up 2ft, then block A should move down 2ft (the rope must "move" 2ft too right?)."
No, there is a difference between a movable pulley and a fixed pulley, so A moves down 1 ft.
"3.Where did 2vA=−vB come from?"
From the same assumption as above. However, the direction of vA is shown incorrectly (or, alternatively, the signs in the formula are wrong).
"4 The FBD for block A is confusing, why is the friction force FA in the direction of the ropes? I thought it was block B that is going down?"
It is writen in the statement of the problem that block B went up.
" Am I the only one who had trouble deducting that the pulley and block A are the same object?"
I don't quite understand what this phrase means exactly and how it is relevant.
"5.Look at the final answer, how could vb be negative? The problem says block B goes UP."
See the answer to your item 3. 
