Coin sliding on a table slides across an expanding fabric tape

[yo yo]

Homework Statement

why is the vector v subtracted at the beginning of the movement, and added at the departure from the fabric? I mean, it's clear why we're subtracting, but the fabric has already been transferred... An impulse? then why are we subtracting?
(the original is in Russian so Fтр is the power of friction, u отн is relative speed and u к is final speed)

Relevant Equations

idk

 

[haruspex]

It is subtracted at the start to find the velocity relative to the ribbon on entry so that the exit velocity relative to the ribbon can be calculated. But to equate that to the given exit velocity, we have to get it back to being relative to the table. To do that we must add the velocity of the ribbon.