The three displacement vectors in the drawing have magnitudes of A = 4.95 m, B =

Question

The three displacement vectors in the drawing have magnitudes of

A = 4.95 m, B = 4.60 m, and C = 3.85 m.

Find the resultant (magnitude and directional angle) of the three vectors by means of the component method. Express the directional angle as an angle above or below the positive or negative x axis. (Assume = 18° and = 68°. Give an answer between 0 and 90°.)

---Select--- below the negative x axis below the positive x axis above the negative x axis above the positive x axis

---Select--- below the negative x axis below the positive x axis above the negative x axis above the positive x axis

Explanation / Answer

According to the question

We know that

Here,

Net horizontal displacement = 4.60cos68 - 4.95cos18 = - 2.98m

Then,

Net vertical displacement = 4.60sin68+ 4.55sin18 - 3.85 = 2.58 m

= directional angle =   tan-1(2.58/2.98)

= 40.88 degree

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