What is the terminal speed for an 84.0kg skier going down a 37.0degree snow-covered slope on wooden skis μk= 0.060? Assume that the skier is 1.80m tall and 0.300m wide.

Okay, here is a solution. Not sure if it's the best one, but it seems to work.

D = drag force
D = (1/4)Av^2 v is terminal velocity
A = 1.80m * 0.300m

F(net) = D since there is no acceleration

m*g*sinè - ì(kinetic)*m*g*cosè = (1/4)Av^2

solve for v (your terminal velocity)

Your answer should be in the high 50s

those funky è letters are supposed to be theta. The funky ì is mu.

3380.99

To calculate the terminal speed of the skier, we need to consider the forces acting on the skier. These forces include gravity, the normal force, and the force of friction.

1. Start by calculating the gravitational force acting on the skier. The formula for gravitational force is Fg = mg, where m is the mass of the skier (84.0 kg) and g is the acceleration due to gravity (approximately 9.8 m/s^2). Therefore, Fg = (84.0 kg)(9.8 m/s^2).

2. Calculate the normal force. The normal force (Fn) is the force exerted perpendicular to the surface. On a sloped surface, Fn can be calculated using the formula Fn = mg cos(θ), where θ is the angle of the slope (37 degrees) and cos is the cosine function. Therefore, Fn = (84.0 kg)(9.8 m/s^2) * cos(37 degrees).

3. Determine the force of friction. The force of friction (Ff) opposes the motion of the skier. It can be calculated using the formula Ff = μkFn, where μk is the coefficient of kinetic friction (0.060) and Fn is the normal force calculated in the previous step. Therefore, Ff = (0.060)(Fn).

4. Calculate the net force acting on the skier. The net force is the difference between the gravitational force and the force of friction. It is given by Fnet = Fg - Ff.

5. At terminal speed, the net force is zero. Therefore, set Fnet equal to zero and solve for the velocity (terminal speed) of the skier.

6. To find the terminal speed, divide the mass of the skier by the cross-sectional area of the skier. The cross-sectional area can be approximated by multiplying the skier's height (1.80 m) by their width (0.300 m).

By following these steps, you can determine the terminal speed for the given skier going down the slope on wooden skis.