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mia_material_x1

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**http://imgur.com/luj32IE 1. Homework Statement**

A skier starts from rest at the top of a smooth incline of height 20 m as in Figure 2. At the bottom of the

incline, the skier encounters a horizontal rough surface where the coecient of kinetic friction between the

skis and the snow is 0.21.

(a) How far does the skier travel on the horizontal surface before coming to rest?

(b) Find the horizontal distance the skier travels before coming to rest if the incline is also rough with a coecient of kinetic friction equal to 0.21.

## Homework Equations

*Vf² = Vi² + 2a(Xf - Xi)*

K = MV²/2

K = MV²/2

## The Attempt at a Solution

*Yi =H= 20m*

θ = 20°

uk = 0.21

θ = 20°

uk = 0.21

a) Vf² = Vi² - 2g(Yf-Yi)

Vf² = 0 - 2g(0-20m)

Vf = 19.8 m/s

*Ke2 - Ke1 = A(friction)*

Ke2 - Ke1 = 0 - MV²/2 = - MV²/2

A(f) = F×S×cos(180°-20°)

- MVf²/2 = F×S×cos(180°-20°)

- MVf²/2 = (uk)(Mg)S(cos160°)

S =

**101m**b) MVf²/2 = (uk)(Mg)S

S= Vf²/2(ukg) = (19.8m/s) / 2(0.21)(9.8m/s²) =

**95m**

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