A 64.9 kg skier coasts up a snow-covered hill that makes an angle of 25.4° with the horizontal. The initial speed of the skier is 8.67 m/s. After coasting a distance of 1.92 m up the slope, the speed of the skier is 4.33 m/s. Calculate the work done by the kinetic frictional force that acts on the skis.

To calculate the work done by the kinetic frictional force, we need to first determine the net work done on the skier. The work done by the kinetic frictional force is defined as the negative of the net work done on the skier.

The net work done on an object can be calculated using the work-energy principle, which states that the net work done on an object is equal to the change in its kinetic energy.

The change in kinetic energy (ΔK) can be calculated using the following formula:
ΔK = Kfinal - Kinitial
where Kfinal is the final kinetic energy of the skier and Kinitial is the initial kinetic energy of the skier.

The formula for calculating the kinetic energy of an object is:
K = (1/2) * m * v^2
where m is the mass of the object and v is its velocity.

In this problem, we are given the initial speed of the skier (vinitial = 8.67 m/s) and the final speed of the skier (vfinal = 4.33 m/s). We are also given the mass of the skier (m = 64.9 kg).

First, let's calculate the initial and final kinetic energies of the skier using the given information:

Kinitial = (1/2) * m * vinitial^2
Kinitial = (1/2) * 64.9 kg * (8.67 m/s)^2

Kfinal = (1/2) * m * vfinal^2
Kfinal = (1/2) * 64.9 kg * (4.33 m/s)^2

Now, let's substitute the values and calculate Kinitial and Kfinal:

Kinitial = (1/2) * 64.9 kg * (8.67 m/s)^2
Kinitial ≈ 2541.30 J

Kfinal = (1/2) * 64.9 kg * (4.33 m/s)^2
Kfinal ≈ 746.99 J

The change in kinetic energy (ΔK) can be calculated by subtracting Kinitial from Kfinal:

ΔK = Kfinal - Kinitial
ΔK ≈ 746.99 J - 2541.30 J
ΔK ≈ -1794.31 J

Since the work done by the kinetic frictional force is defined as the negative of the net work done on the skier, the work done by the kinetic frictional force (Wfriction) can be calculated as:

Wfriction = -ΔK
Wfriction ≈ -(-1794.31 J)
Wfriction ≈ 1794.31 J

Therefore, the work done by the kinetic frictional force that acts on the skis is approximately 1794.31 Joules.