2. The three displacement vectors in the drawing have magnitudes of A = 5.40 m,

Question

2.  The three displacement vectors in the drawing have magnitudes of A = 5.40 m, B = 5.35 m, and C = 4.42 m. Find the resultant
((a) magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis.

Your friend has slipped and fallen. To help her up, you pull with a force as the drawing shows. The vertical component of this force is 148 newtons (N), while the horizontal component is 154 N. Find (a) the magnitude of and (b) the angle The three displacement vectors in the drawing have magnitudes of A = 5.40 m, B = 5.35 m, and C = 4.42 m. Find the resultant magnitude and (b) directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above the positive or negative x axis.

Explanation / Answer

a) magnitude = sqrt ( 148^2 + 154^2 ) = 213.59N

b) direction = arctan(148/154) = 43.86 degrees

2. a) Ax = -5.4 cos(20) = -5.074; Ay = 5.4 sin(20) = 1.847

Bx = 5.35 cos(60) = 2.675; By = 5.35 sin(60) = 4.633

Cx = 0.0; Cy = -4.42

So, summing the coordinates: Rx = -2.399 and Ry = 2.06

So, magnitude = sqrt(2.399^2 + 2.06^2) = 3.162

Direction = arctan(2.06/2.399) = 40.65 degrees

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