The Solution to the Skier Problem:  Use energy conservation throughout.  

mgh (energy at top) = ½ mv² + F_fd  (energy at bottom of hill)  = F_fs (energy along horizontal)

                                         mgh = ½ mv² + µmgCosqd = µmgs

Let d = h/Sinq

                                         mgh = ½ mv² + µmgCosqh / Sinq = µmgs

Subtract the energy consumed by friction going down the hill which eliminates from the problem the kinetic energy at the bottom.

                                         mgh - µmgCosqh / Sinq = µmgs

                                         h - µCosqh / Sinq = µs

                                         s =  [h - µCosqh / Sinq] / µ    or     [h (1 - µCotq)] / µ

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