A vector A has a magnitude of 60.0 m and points in a direction 20.0° belowthe po

Question

A vector A has a magnitude of 60.0 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 53.0° 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 = 60 cos 20 i + 60 sin 20 j                = 56.38 i + 20.52 j Vector B = 70 cos 53 i + 70 sin 53 j              = 42.12 i + 55.90 j So, vector C = ( 56.38 + 42.12 ) i + ( 20.52 + 55.9 )j                     = 98.5 i + 76.42 j Let the C vector makes an with X-axis tan = 76.42 / 98.5         = 37.8degrees

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