Solving for Speed of Extreme Skier Descending Mountain

[rcmango]

Homework Statement

An extreme skier, starting from rest, coasts down a mountain that makes an angle 25.0° with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts for a distance of 12.3 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 3.70 m below the edge. How fast is she going just before she lands?

Homework Equations

The Attempt at a Solution

W = KEf -KE0
(1/2mv^2 - 1/2m* v^20)

 

[catkin]

Conservation of energy does not apply when there is friction unless you include the heat generated by the friction.

To solve this problem you need to use the friction.

It's a 3 stage problem and only the last can be solved by conservation of energy: 1) an acceleration down ramp 2) a deceleration along the horizontal from bottom of ramp to edge of cliff and 3) a vertical acceleration while horizontal velocity is unchanged.

 

[Astronuc]

Well from the distance traveled and the angle, one can determine the change in elevation of the skier on the mountain. If the snow was frictionless, then this change in elevation (change in gravitational potential energy, GPE) would be transformed into kinetic energy (conservation of energy). However, there is a dissipative force - friction - which does work against the skier, so this work has to be subtracted from the GPE to find the KE at the point where the skier leaves the cliff. Knowing the KE, one determines the velocity, which is the initial velocity for the second part of the problem where the skier is in free fall for 3.7 m.

Note that since the skier's velocity is at 25° with respect to horizontal, there is both a horizontal and vertical component to the velocity.