Two forces, F1 vec and F2 vec, act at a point. F1 vec has a magnitude of 9.60 N and is directed at an angle of 55.0∘ above the negative x axis in the second quadrant. F2 vec has a magnitude of 5.40 N and is directed at an angle of 53.1∘ below the negative x axis in the third quadrant. A. What is the x component of the resultant force?B. What is the y component of the resultant force?C. What is the magnitude of the resultant force?

A.

B.

C.

Explanation:

First, we break down the two vectors F₁ and F₂ into their components. In order to do that, we have to use trigonometry:

(Note: , and are negative because the vectors are in the second and third quadrant, respectively. So those components must be negative)

Next, we sum the x components and the y components to get the components of the resultant force:

So, the x component of the resultant force is -8.74N (A), and its y component is 3.55N (B).

Finally, to get the magnitude of the resultant force, we have to use the Pythagorean Theorem:

In words, the magnitude of the resultant force is 9.43N (C).

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