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## Homework Statement

A skier traveling 12.6 m/s reaches the foot of a steady upward 15.2° incline and glides 12.0 m up along this slope before coming to rest. What was the average coefficient of friction?

## Homework Equations

## The Attempt at a Solution

D = 12m

Velocity initial = 12.3 m/s

V final = 0 m/s

Angle = 15.2° incline

Use the equation Vf^2 = Vi^2 + 2*a*d

Find a

0 = 12.3^2 + 2*a*12

2*a*12 = -12.3^2

Divide both sides by 2*12

a = 6.30375 m/s^2

Force parallel = mass * g * sin θ

Force normal = mass*g* cos θ

Friction Force = µ * mass*g* cos θ

Going up an incline 2 forces decrease your velocity

Force parallel and Friction, so we add these 2 forces to find the total force decreasing your velocity. Since these forces decrease your velocity they are negative.

a = 6.30375 m/s^2

∑ Forces = mass * acceleration

(-mass * g * sin θ) + -(µ * mass*g* cos θ) = mass * 6.30375

Notice mass cancels

(- g * sin 15.2°) + (-µ * g* cos 15.2° ) = 6.30375

6.30375 = -2.57 + -9.457 µ

6.30375 = -12.027 µ

µ = 0.524

But the answer is incorrect. Can someone please tell me where I messed up?