A skier travelling at 14 m s-1 reaches the foot of a steady upward 14° incline and glides 21 m along this slope before coming to rest.

What was the average coefficient of friction?

To find the average coefficient of friction, we can use the concept of work and energy. The work done against friction can be calculated, which can then be used to find the average coefficient of friction.

First, let's calculate the work done against friction. We know that the work done is equal to the force of friction multiplied by the distance traveled along the incline. In this case, the distance traveled along the incline is given as 21 m.

The work done against friction (W_friction) is given by the equation:
W_friction = f_friction * d

Next, we need to calculate the force of friction (f_friction) using the formula:
f_friction = μ * N

Here, N represents the normal force acting on the skier, which is equal to the product of the skier's mass (m) and the acceleration due to gravity (g). The formula is:
N = m * g

Using the given information, we can calculate the normal force and the force of friction.

Now, we can substitute the values into the equation for work done to find the work done against friction.

Finally, we can calculate the average coefficient of friction (μ) using the equation:
μ = W_friction / (m * g * d)

Substituting the values, we can find the average coefficient of friction.