A force of 12 N acts at 45° to the +x axis. Which set of component values matches F_x and F_y?

• A. F_x = 6.00 N, F_y = 6.00 N
• B. F_x = 10.70 N, F_y = 10.70 N
• C. F_x = 0 N, F_y = 12 N
• D. F_x = 8.49 N, F_y = 8.49 N

Answer: (D)

When a force is angled relative to the x-axis, its x and y components come from projecting the force onto the axes: F_x = F cos θ and F_y = F sin θ, with θ measured from the +x direction. For a 12 N force at 45°, cos 45° and sin 45° are both √2/2 ≈ 0.707. So F_x = 12 × 0.707 ≈ 8.49 N and F_y = 12 × 0.707 ≈ 8.49 N. Since the angle is in the first quadrant, both components are positive. The components are equal, giving (8.49 N, 8.49 N), which is the correct match. The other options don’t fit because they imply different projections: angles that aren’t 45° or magnitudes that don’t align with 12 N when projected, so their component values don’t match F cos 45° and F sin 45°.