A vector A has a magnitude of 45.0 m and points in a direction 20.0° belowthe po

Question

A vector A has a magnitude of 45.0 m and points in a direction 20.0° belowthe positive x axis. A second vector, B,has a magnitude of 70.0 m and points in a direction 59.0° above the positive x axis. (a) Sketch the vectors A,B, and C = A +B. (Do this on paper. Your instructor may ask youto turn in this diagram.)

(b) Using the component method of vector addition, find themagnitude and direction of the vector C.
2 m
3° (counterclockwise from the positivex-axis)
(a) Sketch the vectors A,B, and C = A +B. (Do this on paper. Your instructor may ask youto turn in this diagram.)

(b) Using the component method of vector addition, find themagnitude and direction of the vector C.
2 m
3° (counterclockwise from the positivex-axis)

Explanation / Answer

Vector A = 45 cos 20 i + 45 sin 20 j                = 42.28 i + 15.39 j Vector B = 70 cos 59 i + 70 sin 59 j              = 36.35 i + 60 j So, vector C = ( 42.28+36.35 ) i + ( 15.39+ 60 ) j                     = 78.63 i + 75.39 j Let the C vector makes an with X-axis tan =  75.39 / 78.63         = 43.79degrees

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