A 64.2-kg skier coasts up a snow-covered hill that makes an angle of 23.8° with the horizontal. The initial speed of the skier is 7.18 m/s. After coasting 1.96 m up the slope, the skier has a speed of 3.13 m/s. Calculate the work done by the kinetic frictional force that acts on the skis.

when up vertically 1.96 sin 23.8

call that h = 1.96 sin 23.8
gain in potential energy = m g h

inital Ke = (1/2) m (7.18)^2 = initial total Energy
final total energy = (1/2)m(3.13)^2+m g h

loss to friction = inital total - final total

= (1/2)m(7.18^2-3.13^2) -mgh

-842.72 J

To calculate the work done by the kinetic frictional force, we need to use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy.

We can break down the problem into two parts: the work done by the skier's initial kinetic energy and the work done by the frictional force.

1. Work done by the skier's initial kinetic energy:
The initial kinetic energy of the skier is given by:
KE_initial = 1/2 * m * v_initial^2,
where m is the mass of the skier (64.2 kg) and v_initial is the initial speed of the skier (7.18 m/s).
Plugging in the values, we get:
KE_initial = 1/2 * 64.2 kg * (7.18 m/s)^2.

2. Work done by the frictional force:
The work done by the frictional force is equal to the change in kinetic energy of the skier:
Work_friction = KE_final - KE_initial,
where KE_final is the final kinetic energy of the skier.
The final kinetic energy of the skier can be calculated using the final speed:
KE_final = 1/2 * m * v_final^2,
where v_final is the final speed of the skier (3.13 m/s).
Plugging in the values, we get:
KE_final = 1/2 * 64.2 kg * (3.13 m/s)^2.

Now we can calculate the work done by the frictional force:
Work_friction = KE_final - KE_initial.

To conclude, plug in the values for the initial and final speeds of the skier, as well as the mass, into the equations to 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 use the work-energy principle. According to this principle, the work done is equal to the change in kinetic energy.

The initial kinetic energy of the skier can be calculated using the formula: KE_initial = 1/2 * m * v_initial^2, where m is the mass of the skier and v_initial is the initial speed of the skier.

KE_initial = 1/2 * 64.2 kg * (7.18 m/s)^2
KE_initial = 1643.34204 J (rounded to four decimal places)

The final kinetic energy of the skier can be calculated similarly using: KE_final = 1/2 * m * v_final^2, where v_final is the final speed of the skier.

KE_final = 1/2 * 64.2 kg * (3.13 m/s)^2
KE_final = 625.03257 J (rounded to four decimal places)

Now, the work done by the kinetic frictional force can be calculated by taking the difference between the initial and final kinetic energy:

Work = KE_final - KE_initial
Work = 625.03257 J - 1643.34204 J
Work = -1018.30947 J (rounded to four decimal places)

The negative sign indicates that the work done by the kinetic frictional force is in the opposite direction of the skier's motion.