Answer
The magnitude of the average velocity is $~~2.3~cm/min$
Work Step by Step
We can find the displacement of the center of the rope in units of $cm$:
$x = 3.7~m = 370~cm$
We can find the time of the contest in units of minutes:
$t = 2~h~41~min = 120~min+41~min = 161~min$
We can find the magnitude of the average velocity:
$v_{ave} = \frac{\Delta x}{\Delta t} = \frac{370~cm}{161~min} = 2.3~cm/min$
The magnitude of the average velocity is $~~2.3~cm/min$.
