Block and Pulley Velocities

1. The problem statement, all variables and given/known data
Find V if the pulley is massless, friction less and

Can take any no of variables but V is be in terms of VP.Ignore gravity and other forces

2. The attempt at a solution
If Pulley comes down by X, the length of string towards left will increase by 2X
Therefore, If in same time pulley comes down by VP, String will increase at rate of V=2VP.
.’. the answer is V=2VP
But the answer is given wrong
The answer in key states V = VP(1+cosβ)
(where β is angle between pulley and increasing string-Left string)

Attached Images
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