A skier traveling 9.4 m/s reaches the foot of a steady upward 16 ∘ incline and glides 12 m up along this slope before coming to rest. What was the average coefficient of friction?

The  average coefficient of friction is 0.104

Explanation:

Given;

velocity of the skier, v = 9.4 m/s

angle of inclination, θ = 16°

height of the slope, h = 12 m

Calculate the kinetic energy of the skier at the given velocity;

KE =¹/₂mv²

KE = ¹/₂m(9.4)²

KE = 44.18m

Calculate the potential energy of the skier up the slope;

PE = mghsinθ

PE = m x 9.8 x 12 x sin16

PE = 32.411 m

Calculate the friction force on the inclined plane;

Fk = μk x mgCosθ

Fk =  μk x m x 9.8 x Cos16

Fk =  μk x m x 9.421

Calculate the work done by friction;

Work done = Fk x d

Work done = μk x m x 9.421 x d

Work done = μk x m x 9.421 x 12

Work done = 113.052mμk

Apply the principle of conservation of energy;

KE = PE + work done by friction

44.18m = 32.411 m + 113.052mμk (factor out m and divide through by it)

44.18 = 32.411  + 113.052μk

44.18 - 32.411  = 113.052μk

11.769 = 113.052μk

μk = 11.769 / 113.052

μk = 0.104

Therefore, the  average coefficient of friction is 0.104

carla slowed down in the beginning of her trip, stopped, and then sped up

the displacement produced by the body.  

the amount of force subjected to the body.  

the angle between the direction of force and displacement