Question #14628

The force vector A has a magnitude of 71.0 newtons (N) and points due east. The force vector B has a magnitude of 145 N and points 74.0 ° north of east. Find the (a) magnitude and (b) direction of A - B. (Give the direction as a positive angle with respect to due east). Find the (c) magnitude and (d) direction of B - A. (Give the direction as a positive angle with respect to due west).

Expert's answer

A = 71N i + 0N j

B = 145Ncos74 i + 145Nsin74 j = 40N i + 139N j

A - B = (71 - 40)N i - 139N j = 31N i - 139N j

R = √(31² + 139²) = 142 N

Θ = tan^{-1}(-139/31) = -77º = 283º w/r/t East (quadrant IV)

B - A = -31N i + 139 j

R = 142 N

Θ = -77º w/r/t West = 283º w/r/t West (quadrant II)

B = 145Ncos74 i + 145Nsin74 j = 40N i + 139N j

A - B = (71 - 40)N i - 139N j = 31N i - 139N j

R = √(31² + 139²) = 142 N

Θ = tan

B - A = -31N i + 139 j

R = 142 N

Θ = -77º w/r/t West = 283º w/r/t West (quadrant II)

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