Final answer:
The change in velocity of the speed skater hitting a rough ice patch is -2.8 m/s.
Step-by-step explanation:
To calculate the change in velocity of the speed skater, we can use the equation:
Change in velocity = final velocity - initial velocity
Plugging in the given values, we have:
Change in velocity = 5.3 m/s - 8.1 m/s
Simplifying, we get:
Change in velocity = -2.8 m/s
Therefore, the change in velocity from 8.1 m/s to 5.3 m/s over a 4.4-m-wide patch is -2.8 m/s.