Aperson with a mass of 75 kg skis from rest down a slope at an angle of 31 degrees. the coefficient of kinetic friction of his skis on the snow is 0.095. what is his acceleration?

4.2 m/s²

Explanation:

Draw a free body diagram.  There are three forces on the skier:

Weight force mg pulling down

Normal force N perpendicular to the incline

Friction force Nμ parallel up the incline

Sum of the forces perpendicular to the incline:

∑F = ma

N − mg cos θ = 0

N = mg cos θ

Sum of the forces parallel to the incline:

∑F = ma

mg sin θ − Nμ = ma

Substitute:

mg sin θ − mgμ cos θ = ma

g sin θ − gμ cos θ = a

a = g (sin θ − μ cos θ)

Plug in values:

a = (9.8 m/s²) (sin 31° − 0.095 cos 31°)

a = 4.2 m/s²

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