A person 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