## Step-by-Step Solution ### **Given:** - Magnitude of force vector, \( F = 25. \) N - Angle, \( \theta = 40.^\circ \) west of south - Positive x-axis = east, positive y-axis = north ### **Step 1: Visualize the Direction** - "West of south" means start pointing south (down along the negative y-axis) and rotate 40.° towards the west (negative x-axis). ### **Step 2: Break the Force into Components** The x-component (east-west) is what we need. Let’s use trigonometry: - The angle from the south axis is 40.° towards west, so the x-component will be: \[ F_x = F \sin(40.^\circ) \] **Note:** It's negative because it's towards west (negative x). ### **Step 3: Plug in the Values** \[ F_x = 25. \cdot \sin(40.^\circ) \] \[ \sin(40.^\circ) \approx .6428 \] \[ F_x = 25. \cdot .6428 \approx 16.07 \] But since it's to the west (negative x): \[ F_x = -16.1 \text{ N} \] ### **Step 4: Final Answer** \[ \boxed{-16.1\, \text{N}} \] **So, the correct answer is:** **C. –16.1 N**