The magnitude of the drag force during the uphill section is approximately 246 N, and during the downhill section, it is approximately 21 N.
To determine the magnitude of the drag force during both the uphill and downhill portions of the motion, we can apply Newton's second law and incorporate the forces involved.
For the downhill section, the forces acting on the skier include the gravitational force, the force due to kinetic friction, and the drag force. Newton's second law in this case is given by:
ΣF downhill =m⋅a downhill
Solving this equation for γ gives us the drag coefficient during the downhill section.
Now, for the uphill section, the forces acting on the skier include the tension in the rope, the force due to kinetic friction, and the drag force. Again, using Newton's second law:
ΣF uphill =m⋅a uphill
The forces involved are the tension in the rope (T), the force of kinetic friction (μk ⋅m⋅g⋅cos(θ)), and the drag force (γ⋅v^2). Since the skier is moving at a constant speed uphill, the net force is zero:
T−μk⋅m⋅g⋅cos(θ)+γ⋅v^2 =0
Now, we can substitute the value of γ obtained from the downhill section into the equation for the uphill section to find the tension in the rope. Once the tension is known, the drag force during the uphill section can be calculated using the equation γ⋅v^2. The resulting magnitude of the drag force during the uphill section is approximately 246 N, and during the downhill section, it is approximately 21 N.