The displacement vectors A rightarrow and B rightarrow shown in the figure below

Question

The displacement vectors A rightarrow and B rightarrow shown in the figure below both have magnitudes of 2.74 m. The direction of vector A rightarrow is 18.2 degree. Find A rightarrow + B rightarrow graphically. magnitude m direction degree counterclockwise from the +x axis Find A rightarrow - B rightarrow graphically. magnitude m direction degree counterclockwise from the +x axis Find B rightarrow - A rightarrow graphically. magnitude m direction degree counterclockwise from the +x axis Find A rightarrow - 2B rightarrow graphically, magnitude m direction degree counterclockwise from the +x axis

Explanation / Answer

Vertical displacement of A
Ay = 2.74sin18.2
Ay = 0.855 m

Horizontal displacement of A
Ax = 2.74cos18.2
Ax = 2.602

a) Horizontal displacement of A + B = 2.602 + 0 = 2.602
Vertical displacement of A + B = 0.855 + 2.74 = 3.595
A + B vector length = (2.602² + 3.595²) = 4.43m
Angle of A + B
tan = 4.43 / 2.602
= 59.53relative to the x axis

b) Horizontal displacement of A - B = 2.602 - 0 = 2.602
Vertical displacement of A - B = 0.855 - 2.74 = -1.885
A - B vector length = (2.602² + 1.885²) = 3.21 m
Angle of A - B
tan = -1.885/ 2.602
= -35.75° relative to the x axis

c) Horizontal displacement of B - A = 0 - 2.602 = -2.602
Vertical displacement of B - A = 2.74 - 0.855 = 1.885
B - A vector length = (2.602² + 1.885²) = 3.21 m
Angle of B - A
tan = 1.885/ -2.602
= 144.25° relative to the x axis after adjusting for quadrant

d) Horizontal displacement of A - 2B = 2.602 - 2(0) = 2.602
Vertical displacement of A - 2B = 0.855 - 2(2.74) = -4.625
A - 2B vector length = (2.602² + 4.625²) = 5.306 m
Angle of A - 2B
tan = -4.625/ 2.602
= -60.53° relative to the x axis

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