# Physics

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Multiple Concept Example 9 provides background pertinent to this problem. The magnitudes of the four displacement vectors shown in the drawing are A = 16.0 m, B = 12.0 m, C = 13.0 m, and D = 23.0 m. Determine the (a) magnitude and (b) direction for the resultant that occurs when these vectors are added together. Specify the direction as a positive (counterclockwise) angle from the +x axis.

• Physics -

no drawing.

• Physics -

A(x) = - 16•cos 20º = - 15.03,
A(y) = 16•sin 20º = 5.47,
B(x) = 0,
B(y) = 11,
C(x) = - 12•cos 35º = - 9.83,
C(y) = - 12•sin 35º =- 6.88,
D(x) = 26•cos 50º = 16.71,
D(y) = - 26•sin 50º =- 19.92.
M(x) = A(x)+B(x) +C(x) +D(x) = -15.03 + 0-9.83 +16.71 = - 8.12.
M(y) = 5.47 + 11 = 6.88 -19.92 = - 10.33.
M= sqrt{M(x)² + M(y)²} = sqrt (8.12²+ 10.33²) =13.14.
tan α = M(y)/M(x) = 10.33/8.12 =1.27.
α = 51.8º.
angle is 180 – 51.8 =128.2º (counterclockwise angle from the +x axis)

• Physics -

@Elena, I got M(y) = 3.438 rather than -10.33. I think mine is correct, but please correct me if I'm wrong!

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