Consider the skateboarder in the figure below. If she has a mass of 57 kg, an initial velocity of 21 m/s, and a velocity of 10 m/s at the top of the ramp, what is the work done by friction on the skateboarder? Ignore the kinetic energy of the skateboard's wheels. The skateboarder reaches a maximum height of 5 m.

To find the work done by friction on the skateboarder, we need to calculate the change in kinetic energy.

The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the work done by friction will cause a decrease in kinetic energy as the skateboarder moves up the ramp.

Given:
- Mass of skateboarder (m) = 57 kg
- Initial velocity (v_initial) = 21 m/s
- Velocity at the top of the ramp (v_final) = 10 m/s
- Maximum height reached (h) = 5 m

First, we need to find the initial kinetic energy (KE_initial) and the final kinetic energy (KE_final) of the skateboarder.

KE_initial = (1/2) * mass * initial velocity^2
KE_initial = (1/2) * 57 kg * (21 m/s)^2

Next, we find the final kinetic energy using the velocity at the top of the ramp.

KE_final = (1/2) * mass * final velocity^2
KE_final = (1/2) * 57 kg * (10 m/s)^2

To find the change in kinetic energy, we simply subtract the final kinetic energy from the initial kinetic energy.

Change in KE = KE_final - KE_initial

Now that we have the change in kinetic energy, we can determine the work done by friction. Since the work done by friction is negative (opposite to the direction of motion), we can write:

Work done by friction = - Change in KE

By plugging in the values, we can calculate the work done by friction.