Graphically determine the resultant of the following three vector displacements:

Question

Graphically determine the resultant of the following three vector displacements: (1) 24 m, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south. Determine the resultant length. Determine the resultant direction. Graphically determine the resultant of the following three vector displacements: (1) 24 m, 36 degrees north of east; (2) 18 m, 37 degrees east of north; and (3) 26 m, 33 degrees west of south. Determine the resultant length. Determine the resultant direction.

Explanation / Answer

Here, for the net displacement

let east is the positive x direction

and north is the positive y direction

for the net displacemnet

d = 24 * (cos(36) i + j * sin(36 degree)) + 18 * ( sin(27 degree) i + j * cos(27 degree)) + 26 * (- sin(33) i - j * cos(33))

d = 13.43 i + 8.34 j

resultant length = sqrt(13.43^2 + 8.34^2)

resultant length = 15.8 m

the resultant length is 15.8 m

resultant direction = arctan(8.34/13.43)

resultant direction = 31.8 degree

the resultant direction is 31.8 degree north of east

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