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Vector displacement problem (Physics)

Consider two vectors F~
1 with magnitude 81 N
inclined at 281?
and F~
2 with magnitude 52 N
inclined at 228?
, measured from the positive
x axis with counterclockwise positive.
What is the magnitude of the resultant vector
1 + F~
2 ? Draw the vectors to scale on a
graph to determine the answer.
Answer in units of N. Your answer must
be within ± 5.0%

1 Answer by Expert Tutors

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George M. | Tutor in Physics, Science, Math. (MS Physics, UT Dallas)Tutor in Physics, Science, Math. (MS Ph...
5.0 5.0 (4 lesson ratings) (4)
Hi Sofia!
I am going to leave part of the problem for you to work.
Step 1: We break each vector into its x and y components using the trigonometry of sines and cosines.  Make sure to pay attention to the positive and negative signs when doing this.
F1x=F1[cos(281)]=81N(        )         
F2x=F2[cos(228)]=52N(        )
F1y=F2[sin(281)]=81N(        )
F2y=F2[sin(228)]=52N(        )
Step 2: We add the x-components to get the x component of the resultant vector.
Step 3: We add the y-components to get the y component of the resultant vector.
Step 4: We use the Pythagorean Theorem to compute the magnitude of the resultant from the x and y components of the resultant.
R=SQR [Rx2+Ry2]
Step 5: We find the angle that R makes with the nearest x-axis from tan(theta)=(Ry/Rx), so   theta=arctan(Ry/Rx)