Two snowy peaks are 990 m and 890 m above the valley between them. A ski run ext

Question

Two snowy peaks are 990 m and 890 m above the valley between them. A ski run extends down from the top of the higher peak and then back up to the top of the lower one, with a total length of 2.7 km and an average slope of 23.5°. A skier starts from rest on the higher peak. At what speed will she arrive at the top of the lower peak if she just coasts without using the poles? Ignore friction.

b) Approximately what coefficient of kinetic friction between the snow and skis would make the skier stop just at the top of the lower peak?

Explanation / Answer

a) At what speed will she arrive at the top of the lower peak if she just coasts without using the poles?

The difference in heights is delta_H = 990-890 = 100 m

The potential energy that he looses is PE = mg delta_H

The kinetic energy that he gains is 0.5mv^2.

So by equating these energies we get,

0.5mv^2 = mg delta_H

v^2/2 = 100*9.81 = 981

v = 44.29 m/s

b) Approximately what coefficient of kinetic friction between the snow and skis would make the skier stop just at the top of the lower peak?

=delta_H/d = 100/2700 = 0.037

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