Wilson: [This one, in fact, is a math question but the solution require Physics.  Think again if the velocity y' can solely depending on the distance of x, y and z?  We forgot about the "gravity".  Imagine if the wall doesn't exist, how much does the velocity v affecting the falling velocity of the ladder?

Rather than straight down, the force of the falling ladder should be shown on the left diagram, showed in b at the right diagram.  a is the force against the wall. The velocity of y calculated base on vectors a and b, rather than the distance of x, y and z.

Therefore, the x²+y²=z² is not appropriate to calculate the velocity of y. Agree?]