Determine the coefficient of friction between a girl's skis and the snow when she skis down a 20° degree hill and her ending speed is exactly two-fifths of what it would have been if the slope had been frictionless.

To determine the coefficient of friction between the girl's skis and the snow, we can start by understanding the concept of friction.

Friction is the force that opposes the motion between two surfaces in contact. In this case, the girl's skis are in contact with the snow on a 20° degree hill. The force of friction between the skis and the snow is what slows down the girl's speed.

Now, let's break down the problem step by step:

1. We are given that the girl's ending speed on the 20° degree hill is exactly two-fifths of what it would have been if the slope had been frictionless. This means that the frictional force acting on the girl's skis is causing a reduction in speed.

2. In order to determine the coefficient of friction, we need to calculate the acceleration of the girl's skis. We can use Newton's second law of motion: F = m * a, where F is the net force acting on the skis, m is the mass of the girl, and a is the acceleration.

3. The net force acting on the skis can be calculated as the difference between the gravitational force acting down the hill and the frictional force acting up the hill. The gravitational force can be calculated using the equation: F_gravity = m * g * sin(θ), where g is the acceleration due to gravity (approximately 9.8 m/s²) and θ is the angle of the hill (20° in this case).

4. The frictional force can be calculated as: F_friction = μ * F_normal, where μ is the coefficient of friction and F_normal is the normal force acting perpendicular to the slope.

5. The normal force can be calculated as: F_normal = m * g * cos(θ).

6. Substituting the values into the equations, we can find the net force acting on the skis and the acceleration.

7. The coefficient of friction can then be determined as the ratio of the frictional force to the normal force: μ = F_friction / F_normal.

By following these steps and performing the necessary calculations, you can determine the coefficient of friction between the girl's skis and the snow.