Final answer:
The magnitude of the skier's acceleration down a 35-degree slope with a coefficient of kinetic friction of 0.2 is calculated using the paralleled component of gravitational force and the force of kinetic friction. The normal force due to gravity is also considered in the calculation. Using Newton's second law, the net force provides the acceleration when divided by the skier's mass.
Step-by-step explanation:
To calculate the magnitude of the acceleration of the skier, we start by identifying the forces acting on the skier. The gravitational force acting down the slope can be calculated using the component of the skier's weight parallel to the slope, which is mg sin(θ), where m is the mass of the skier, g is the acceleration due to gravity (9.8 m/s2), and θ is the angle of the slope. In this case, θ is 35 degrees.
The force of kinetic friction acting opposite to the skier's motion is given by μk N, where μk is the coefficient of kinetic friction and N is the normal force. Since the skier is on an incline, the normal force is the component of the skier's weight perpendicular to the slope, calculated as mg cos(θ).
Now we combine these two forces to find the net force, which is mg sin(θ) - μk mg cos(θ). The acceleration a can be found using Newton's second law, F = ma. Therefore, the acceleration is (mg sin(θ) - μk mg cos(θ)) / m, which simplifies to g sin(θ) - μk g cos(θ). Plugging in the values g = 9.8 m/s2, θ = 35 degrees, and μk = 0.2, we calculate the acceleration.