Find the sum of these four vector forces: 12.0 n to the right at 35.0° above the horizontal, 31.0 n to the left at 55.0° above the horizontal, 8.40 n to the left at 35.0° below the horizontal, and 24.0 n to the right at 55.0° below the horizontal. (hint: make a drawing of this situation and select the best axes for x and y so that you have the least number of components. then add the vectors, using the component method.)

R = 7,87N to the left at 82,26° above the horizontal

Explanation:

Graph1: situation drawing (attached image)

Graph2: Resulting from the forces on the x '- y' axes (attached image)

Fx' = (12 - 8,4)N = 3,6N to the right at 35° above the horizontal

Fy' = (31 - 24)N = 7N to the left at 55° above the horizontal

Graph 3: Resulting vector of forces (R) on x-y coordinate axes (attached image)

R = Rx i + Ry j

Rx = 3,6Cos(35°) - 7Cos(55°) = -1,06N

Rx = 3,6Sin(35°) + 7Sin(55°) = 7,8N

R = (1,06 -i + 7,8 j ) N

Magnitude of R:

to the left above the horizontal.

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