To calculate the acceleration of the skater on the rough ice, we use the equation
[tex]v^2= u^2 + 2as[/tex]
Here, u is initial speed when she hits the patch of ice and its value is 10 m/s and v is final speed when she left the patch of ice and its value is given 7.0 m/s and s is the width of patch of ice and its value is 5.0 m.
Substituting these values in above equation we get,
[tex](7 m/s) ^2 = (10 m/s)^2 + 2 a \times 5.0 m \\\\ a = \frac{(70 - 100)(m/s)^2 }{ 10 m} = 3.0 m/s^2[/tex].
Thus, the acceleration of skater on the rough ice is [tex]3.0 m/s^2[/tex]
