Friction on a ski slope

If we take a section of the slope with length $\mathrm{d}l$ and angle of inclination $\theta$ , we will find that the kinetic frictional force acting on an object with mass $m$ on that slope section is : $f = \mu mg \cos \theta$ .

And since the height difference is caused by potential energy that is diminished by the frictional work, we can use the work - energy theorem :

$\int_0^L f \,\mathrm{d}l = mg \Delta h$

$\mu mg \int_0^L \cos \theta\, \mathrm{d}l = mg \Delta h$

$\mu \int_0^s \mathrm{d}x = \Delta h$

$\Delta h = \mu s = 210 m$