The rope speed is V when the drooping part is extended by X. Newton's second law For the whole rope system, [mg (x+h)/l-a * mg * (l-x-h)/l] * (dt) = m * (dv) times v * (dt) = dx twice to get [g (x+h)/l.

[(x+h) (1+a)-a * l] (dx) = [l * (dv 2)]/(2g) and then get [(x+h) (1+a)-a * l] [d (x+)

The relationship between x and v can be obtained by integrating the two sides, so that x=L-h can get the speed when all of them leave the desktop.