A skier travelling at 13 m s-1 reaches the foot of a steady upward 14° incline and glides 18 m along this slope before coming to rest.

What was the average coefficient of friction?

To find the average coefficient of friction, we need to use the concept of work and energy. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.

In this case, the skier is initially moving with a velocity of 13 m/s and comes to rest after gliding along the slope. The work done on the skier is equal to the frictional force multiplied by the distance over which it acts.

First, let's find the change in kinetic energy of the skier.

The initial kinetic energy (K1) is given by:
K1 = (1/2) * mass * velocity^2

The final kinetic energy (K2) is zero since the skier comes to rest.

The change in kinetic energy (ΔK) is:
ΔK = K2 - K1 = -K1

Next, we need to find the work done on the skier by the frictional force.

The work done (W) is equal to the force of friction (F) multiplied by the distance (d) over which it acts.

Knowing that the change in kinetic energy equals the work done, we have:
ΔK = W

In this case, the work done by the frictional force is negative (since it opposes the motion), so we have:
- K1 = -F * d

Rearranging the equation to solve for the force of friction (F), we get:
F = K1 / d

Now, we can calculate the coefficient of friction (μ) using the formula:
F = μ * N

Where N is the normal force, given by:
N = mass * gravity

We can substitute the expression for F into the above equation:
K1 / d = μ * mass * gravity

Finally, rearranging this equation to solve for the coefficient of friction (μ), we get:
μ = K1 / (mass * gravity * d)

Plugging in the values given, we can now calculate the average coefficient of friction.

Mass of the skier (m) = (We are not provided with the mass.)

We can calculate the average coefficient of friction if we know the mass of the skier. Without this information, we cannot find the exact average coefficient of friction.