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A really steep ski slope

The Manni Pranger ski slope in Austria is one of the steepest slopes which can be groomed by machines; the resort needs to put the machines on a special winch to keep them from sliding down the hill. The average slope is 46 degrees.

Assume that the coefficient of kinetic friction between skis and snow is μ = 0.05 .

  1. What is the acceleration of a skier on this slope?
  2. How long would it take the skier to go from 0 to 60 mph? It takes a Mazda Miata about 8 seconds and a 2010 Ford Mustang about 5.2 seconds.
  3. It's hard to tell the length of this slope, but my best guess from pictures and videos is that the slope has a length of about 1000 meters. How fast would a skier be going at the bottom?

Creative Commons License Copyright © Michael Richmond. This work is licensed under a Creative Commons License.