Velocity – String(Pulley) constraints

1. The problem statement, all variables and given/known data
A bead C can move freely on a horizontal rod. The bead is connected by blocks B and D by a string as shown in the figure. If the velocity of B is v. Find the velocity of block D.

2. Relevant equations
As the string is inextensible the velocity of the string along the length is const.

3. The attempt at a solution
The doubt I have is that, the following should be true
[tex]v_c\ =\ v_b.cos53°\ \ \ \ …(1)[/tex]

But in the solution from the book I get that
[tex]v_b\ =\ v_c.cos53°\ \ \ \ …(2)[/tex]

I used relation 1 and got wrong results, I’m just confused how do we get relation 2.
Kindly help me out.
Thanks for your time 🙂

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