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.

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To calculate the work done by the kinetic frictional force, we need to find the change in kinetic energy of the skier.

The work done by a force can be calculated using the formula:

Work = force * distance * cos(theta)

Where:

- Work is the work done by the force.
- Force is the component of the force acting in the direction of motion.
- Distance is the distance over which the force acts.
- Theta is the angle between the force and the direction of motion.

In this case, the force acting on the skier is the kinetic frictional force. The work done by this force will be negative as the force acts in the opposite direction of motion.

First, we need to find the force of kinetic friction. The force of kinetic friction can be calculated using the formula:

Force of friction = coefficient of kinetic friction * normal force

The normal force is the force exerted by the hill on the skier perpendicular to the surface. It can be calculated using the formula:

Normal force = mass * acceleration due to gravity * cos(theta)

Now, let's calculate the normal force:

Normal force = 64.9 kg * 9.8 m/s^2 * cos(25.4°)

Next, let's calculate the force of kinetic friction using the coefficient of kinetic friction. Assuming the coefficient of kinetic friction is µ:

Force of friction = µ * Normal force

Now, let's calculate the work done by the kinetic frictional force:

Work = -Force of friction * distance * cos(theta)

Substituting the values and calculating the work will give us the answer.