On an essentially frictionless, horizontal ice rink, a skater moving at 3.9 m/s encounters a rough patch that reduces her speed to 48% of her original speed due to a friction force that is 24% of her weight. Use the work—energy theorem to find the length of this rough patch.

d = 2.5 m

Explanation:

The work-energy theorem, states that the change in the kinetic energy of  a body, is equal to the work done on the object, by the net external force on it, as follows:

       

       

In this case, our givens are as follows:v₀ = 3.9 m/s vf = 0.48*3.9 m/s = 1.87 m/s Fnet = 0.24*m*9.8 m/s2.Replacing by the givens in (1) and (2), rearranging and simplifying common terms, we can solve for drp, as follows:

       

     

Ithink the answer would be a