Friction / inclined plane question

[N_L_]

I am having trouble setting up the following problem:

A child slides down a slide with a 28 degree incline, and at the bottom her speed is precisely half what it would have been if the slide had been frictionless. Calculate the coefficient of kinetic friction between the slide and the child.

I drew an FBD. I split gravity up into it's X and Y components. I know that Force friction = Mu k * Force normal. Fg(x) = m*g*sin(28). Fg(y) = m*g*cos(28)

Force normal - m*g*cos(28) = m*acceleration(x) = 0

m*g*sin(28) - Mu k * ( m*g*cos(28) ) = m*acceleration(x)

Any ideas?

 

[Tide]

HINT: How much work does the frictional force do on the slide as it traverses the slope?

 

[phucnv87]

http://photo-origin.tickle.com/image/69/7/0/O/69708125O733857775.jpg