Answer
The proof is below.
Work Step by Step
We know the following:
$v = \sqrt{\frac{F}{\mu}}$
We also know that the force varies based on the height of the cable as follows:
$ F= \mu y g$
Using substitution, we find:
$v = \sqrt{\frac{\mu y g}{\mu}}$
$v =\sqrt{yg}$
