Solving the Energy Problem: Help a Skier Glide!

[netwerky]

energy problem

A skier starts from rest at top of a hill that is inclined at 10.5 degres with respect to the horizontal. The hillside is 200 m long, and the coefficient of fraction between snow and skis is .075. At the bottom of the hill, the snow is level and the ocefficient of fraction is unhanged. How far does the skier glide along the horizontal portion of the snow before coming to rest?

I already figured out velocity for skier at bottom of hill.

I'm stuck on what to do next.

 

[netwerky]

Also, it is required that I use energy methods

 

[physixguru]

What does conservation of mechanical energy say?

 

[HallsofIvy]

Okay, what is the skier's kinetic and potential energies at the top of the hill?
What are they at the bottom of the hill (don't forget to take energy lost to friction into account)?

On the flat, potential energy doesn't change but when he stops all of his kinetic energy has been lost to friction.