Ice Skater's distance traveled on ice (involving net work-kinetic energy theorem)...?

Question

An ice skater of mass m is given a shove on a frozen pond. After the shove she has a speed of v_1 = 2 m/s. Assume that the only horizontal force that acts on her is a slight frictional force between the blades of the skates and the ice.

Use the net work-kinetic energy theorem to find the distance the skater moves before coming to rest. Assume that the coefficient of kinetic friction between the blades of the skates and the ice is u^kin = 0.12. Explain your work. Thanks! :)

Answer 1

The work done by friction is F*d, where F is the frictional force and d is the stopping distance. F = µ*m*g, where µ is coeff of friction, m is the skater's mass; the frictional energy is then

Ef = µ*m*g*d

This must equal the skater's initial kinetic energy which is Ek = 0.5*m*v^2; thus for Ef = Ek:

0.5*m*v^2 = µ*m*g*d

0.5*v^2 = µ*g*d

d = 0.5*v^2 / µ*g