According to question, the situation is shown in the figure For a sufficiently safe horizontal displacement ΔS can be considered straight. If the corresponding length of path element is ΔL, the friction force is given by µmg
ΔS
ΔL
and the work done by the friction force equals times displacement. µmg
ΔS
ΔL
ΔL = µmgΔS Adding up, we find that along the whole path the total work done by the friction force is µmgS. By energy conservation this must equal the decrease mgh is potential energy of skier. Hence, h = µS.