A skier of mass 73.5 kg is pulled up a slope by a motor-driven cable. How much work is required to pull the skier 58 m up a 32° slope (assumed to be frictionless) at a constant speed of 2.0 m/s?

To calculate the work required to pull the skier up the slope, we need to use the formula:

Work = Force × Distance × Cosine(angle)

First, we need to find the force exerted by the cable. This force can be calculated using the equation:

Force = Mass × Acceleration

In this case, the acceleration is zero because the skier is moving at a constant speed. So, the force exerted by the cable is:

Force = Mass × Acceleration = 73.5 kg × 0 m/s² = 0 N

Since the slope is assumed to be frictionless, we don't need to consider any additional forces.

Next, we need to calculate the component of the force in the direction of the displacement. This can be found using the equation:

Force_parallel = Force × Cosine(angle)

Using the given angle of 32°, the force parallel to the slope is:

Force_parallel = 0 N × cos(32°) = 0 N

Now, we can calculate the work required:

Work = Force_parallel × Distance

Substituting the given distance of 58 m, we get:

Work = 0 N × 58 m = 0 J

Therefore, the work required to pull the skier up the slope is 0 Joules. This indicates that no work was done since there was no force parallel to the displacement.