While solving problems involving constrained motion, such as that which the following picture describes, I am always confused about one aspect of the situation in question:
In the above problem, it is given that the ring moves with a velocity of $Vr$ $m/s$ toward the right. This velocity can be resolved into two components, one along the direction of the rope extending from the string(at an angle $θ°$ with the horizontal, as shown)and one along the perpendicular to this direction.
My doubt us this; once we have resolved $Vr$ along the rope, we find that this value is $Vrcosθ$. What is the physical significance of this? I realize that the ring moves in both directions and these vector components give its velocity in those two directions but does this also imply that the rope also moves with a velocity $Vrcosθ$? I am very confused regarding this concept.
Please help. Much thanks in advance :) Regards.
Edit: I posted the picture only to illustrate my point better. This is not a homework question because it relates to the basic concept of resolving vectors.