A vector has a magnitude of 47.0 m and points in a direction 20 degree below the
ID: 2132857 • Letter: A
Question
A vector has a magnitude of 47.0 m and points in a direction 20 degree below the positive x axis. A second vector, has a magnitude of 75 m and points in a direction 56.0 degree above the positive x axis. Sketch the vectors (Do this on paper. Your instructor may ask you to turn in this work.) Using the component method of vector addition, find the magnitude and direction of the vector . magnitude 1 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. m direction 2 Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out all intermediate results to at least four-digit accuracy to minimize roundoff error. (counterclockwise from the +x axis)Explanation / Answer
A=47cos20i-47sin20j=44.165i-16.07j
B=75cos56i+75sin56i=41.94i+62.18j
C=A+B
=86.1i+46.1j
magnitude=|86.1^2+46.1^2|=97.67
direction=tan^-1 (46.1/86.1)=28.1 degrees
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