What is the terminal speed for an 79.0kg skier going down a 42.0 snow-covered slope on wooden skis uk = 0.060

Assume that the skier is 1.60m tall and 0.500m wide.

To calculate the terminal speed of a skier going down a slope, we need to consider the forces acting on the skier. In this case, the main forces are the gravitational force pulling the skier down the slope and the frictional force between the skis and the snow.

First, let's calculate the gravitational force (Fg) acting on the skier. The formula for gravitational force is given by:

Fg = m * g

Where:
m = mass of the skier (79.0 kg)
g = acceleration due to gravity (9.8 m/s^2)

Substituting the given values, the gravitational force can be calculated as follows:

Fg = 79.0 kg * 9.8 m/s^2

Next, we need to calculate the frictional force (Ff) between the skis and the snow. The formula for frictional force is given by:

Ff = uk * N

Where:
uk = coefficient of kinetic friction (0.060)
N = normal force

To calculate the normal force, we need to determine the component of the gravitational force perpendicular to the slope. This can be calculated as:

N = Fg * cos(θ)

Where θ is the angle of the slope. In this case, the angle is not given, so we cannot calculate the normal force directly.

However, since we are interested in the terminal speed, it means the net force on the skier is zero when the terminal speed is reached. At terminal speed, the gravitational force is balanced by the frictional force. So we can set Fg equal to Ff:

Fg = Ff

Substituting the formulas for Fg and Ff, we get:

m * g = uk * N

Since we cannot directly calculate N, we can rearrange the equation to solve for N:

N = (m * g) / uk

Finally, we can substitute the known values for mass (m), acceleration due to gravity (g), and the coefficient of kinetic friction (uk) to calculate the normal force (N). Then, we can substitute N into the formula for frictional force (Ff) to calculate the terminal speed of the skier.