A skier traveling travelling with a magnitude of velocity v approaches a ramp that has an angle of 0. The approach to the ramp is frictionless, but there is friction on the ramp, and the coefficient of kinetic friction between the skis and the ramp is uk. If the skier travels a distance d up the ramp before coming to a stop, what was their initial velocity v? Your answer for v should be in terms of d, g, uk, and 0.

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A skier traveling with a magnitude of velocity \( v \) approaches a ramp that has an angle of \( \theta \). The approach to the ramp is frictionless, but there is friction on the ramp, and the coefficient of kinetic friction between the skis and the ramp is \( \mu_k \). If the skier travels a distance \( d \) up the ramp before coming to a stop, what was their initial velocity \( v \)? Your answer for \( v \) should be in terms of \( d, g, \mu_k, \) and \( \theta \).

**Diagram Explanation:**

The diagram shows a skier moving horizontally with an initial velocity \( v \) towards a ramp inclined at an angle \( \theta \). The ramp is depicted with an arrow indicating the direction of travel, marked with a distance \( d \) along the ramp's surface. The angle \( \theta \) is shown between the horizontal ground and the incline of the ramp. The initial horizontal path is labeled as frictionless, while the ramp surface has a kinetic friction coefficient \( \mu_k \).
Transcribed Image Text:A skier traveling with a magnitude of velocity \( v \) approaches a ramp that has an angle of \( \theta \). The approach to the ramp is frictionless, but there is friction on the ramp, and the coefficient of kinetic friction between the skis and the ramp is \( \mu_k \). If the skier travels a distance \( d \) up the ramp before coming to a stop, what was their initial velocity \( v \)? Your answer for \( v \) should be in terms of \( d, g, \mu_k, \) and \( \theta \). **Diagram Explanation:** The diagram shows a skier moving horizontally with an initial velocity \( v \) towards a ramp inclined at an angle \( \theta \). The ramp is depicted with an arrow indicating the direction of travel, marked with a distance \( d \) along the ramp's surface. The angle \( \theta \) is shown between the horizontal ground and the incline of the ramp. The initial horizontal path is labeled as frictionless, while the ramp surface has a kinetic friction coefficient \( \mu_k \).
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