How does the movement of A affect the movement of B?

[tuloon]

Homework Statement

http://s284.photobucket.com/albums/ll12/toluun/?action=view&current=IMAG0004.jpg

Here is a picture of the problem at hand. I know how to solve the problem however the only thing I don't understand is the relationship between A and B. This means that if A moves to the right 1ft how far will B move downward?

Homework Equations

I know how to solve the problem however the only thing I don't understand is the relationship between A and B. This means that if A moves to the right 1ft how far will B move downward?

The Attempt at a Solution

I first tried thinking that if A moved 1 ft to the right the change in B would be the length of the rope covered. So Xb(change in mass b)= Xa/cos(30).

However this is incorrect I have the solution and the relationship is Xb = Xa * cos(30)
can anyone explain this?

 

[ideasrule]

You know that r*cos(theta)=Xa and r+Xb=constant (said constant being the length of the rope). You can figure out the relationship between Xa and Xb by substitution.

 

[benhou]

You know that r*cos(theta)=Xa and r+Xb=constant (said constant being the length of the rope). You can figure out the relationship between Xa and Xb by substitution.

I have a question, since we are looking for the relationship between the accelerations, we have to differentiate to get it. But when we do, do we differentiate the cos(theta)?