Final answer:
To find the total forces on the skier, the 105 N pulling force is broken into X and Y components using trigonometric functions, then these components are combined with the backward force. The total X force is 22.2 N, and the total Y force is 40.2 N.
Step-by-step explanation:
To determine the total X force (horizontal force) and the total Y force (vertical force) on the skier, we need to decompose the 105 N force that is pulling the skier at a 22.5 degree angle above the horizontal plane into X and Y components, then combine these with the remaining forces acting on the skier.
The X component of the force can be found using the cosine function of the angle: Fx = 105 N × cos(22.5°)
The Y component of the force can be found using the sine function of the angle: Fy = 105 N × sin(22.5°)
To find the total X force on the skier, we subtract the backward force from the horizontal component of the pulling force: Total Fx = Fx - 74.8 N
The Y force is simply the vertical component of the pulling force since no other forces in the vertical direction are given: Total Fy = Fy
Now we compute the values:
Fx = 105 N × cos(22.5°) = 105 N × 0.9239 ≈ 97.0 NFy = 105 N × sin(22.5°) = 105 N × 0.3827 ≈ 40.2 NTotal Fx = 97.0 N - 74.8 N = 22.2 NTotal Fy = 40.2 N