A 10 N force is applied at 30° above the +x axis. What are the components F_x and F_y of the force?

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Multiple Choice

A 10 N force is applied at 30° above the +x axis. What are the components F_x and F_y of the force?

Explanation:
When you break a force into horizontal and vertical parts, you use trigonometry: the horizontal component comes from the cosine of the angle, and the vertical component comes from the sine. For a 10 N force directed 30° above the +x axis, the horizontal part is F cos(30°) and the vertical part is F sin(30°). So F_x = 10 × cos(30°) ≈ 8.66 N and F_y = 10 × sin(30°) = 5.00 N. This also checks out because the vector’s magnitude is sqrt(8.66^2 + 5^2) ≈ 10 N, and both components are positive, as expected for a direction in the first quadrant.

When you break a force into horizontal and vertical parts, you use trigonometry: the horizontal component comes from the cosine of the angle, and the vertical component comes from the sine. For a 10 N force directed 30° above the +x axis, the horizontal part is F cos(30°) and the vertical part is F sin(30°). So F_x = 10 × cos(30°) ≈ 8.66 N and F_y = 10 × sin(30°) = 5.00 N. This also checks out because the vector’s magnitude is sqrt(8.66^2 + 5^2) ≈ 10 N, and both components are positive, as expected for a direction in the first quadrant.

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