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 on the skier, we need to find the net work done by all the forces acting on the skier.

The work done by a force is given by the formula: Work = Force x Distance x cos(angle)

First, let's find the work done by the force of gravity. The work done by the force of gravity can be calculated as the product of the gravitational force (mg) and the vertical distance traveled by the skier along the slope.

Since the skier is moving up the hill, we need to find the component of the gravitational force parallel to the displacement. The component of the gravitational force parallel to the displacement can be calculated using trigonometry:

Force_parallel = mg * sin(angle)

where m is the mass of the skier and g is the acceleration due to gravity.

The vertical distance traveled by the skier is given by the formula: Distance_vertical = Distance * sin(angle)

Now we can calculate the work done by the force of gravity:

Work_gravity = Force_parallel * Distance_vertical

Next, let's find the work done by the kinetic frictional force. Since we know the initial speed and the final speed of the skier, we can calculate the change in kinetic energy using the formula:

Change in kinetic energy = 1/2 * m * (final speed^2 - initial speed^2)

The work done by the kinetic frictional force is equal to the change in kinetic energy, but with a negative sign, since friction always acts in the opposite direction of motion.

Work_friction = -Change in kinetic energy

Finally, to find the net work done by all the forces, we can sum up the work done by the force of gravity and the work done by the kinetic frictional force:

Net work = Work_gravity + Work_friction

Let's plug in the given values and calculate the work done by the kinetic frictional force.