Relative velocity problem with pulleys

[ual8658]

Homework Statement

Homework Equations

Vb/a = Vb - Va

The Attempt at a Solution

I got as far as realizing that the velocity of B depends on A so I wrote out:
2(Xa) + (Xb/a)cos15 = constant

and took the derivative of that equation to get Vb/a = -16.56. I then got stuck as to how to get Vb.

Is Vb/a in the direction of the rope pulling on B and would Vb be in that direction too? Also since Vb/a is at an incline, how would i put it into the relative velocity equation to account for two velocities at incline?

 

[tech99]

Have I missed something here? For every inch that block A descends along the ramp, block B is pulled by 1 inch. This is because the string is of constant length. So B has the same numerical acceleration and speed as A, but acting in the direction of the 15 degree angle as shown. (Velocity and acceleration must be defined in direction).

 

[ual8658]

Have I missed something here? For every inch that block A descends along the ramp, block B is pulled by 1 inch. This is because the string is of constant length. So B has the same numerical acceleration and speed as A, but acting in the direction of the 15 degree angle as shown. (Velocity and acceleration must be defined in direction).

Well the key says that Vb should be 8.53 at an angle of 14.05 degrees on the block. Your explanation makes much more sense so I don't get why the book would say this.