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X an y components of a vector

  • Thread starter jpd5184
  • Start date
  • #1
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Homework Statement



what are the x and y components of a vector a in the xy plane if its direction is 210(degrees) counterclockwise from the positive direction of the x axis and its magnitude is 14 m.

Homework Equations



vector is in the third quadrant with an angle of 30(degrees)

The Attempt at a Solution



i got the angle to be 30(degrees) so i just did

14sin30 for the x component = 7.0
14cos30 for the y component = 12.1

should they both be negative since there in the third quadrant or do the negatives cancel to get a positive.
 

Answers and Replies

  • #2
Char. Limit
Gold Member
1,204
14
Negatives cancel only when you multiply them. Since you aren't multiplying here, both parts are negative.
 
  • #3
76
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would my answers be correct then

x = -7.0

y= -12.1
 
  • #4
Char. Limit
Gold Member
1,204
14
That seems right, yes.

Although, if significant figures were important, the y component might have to be rounded... I'm not sure how important they are here.
 
  • #5
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14.cos 30=x . if it is 30 degree to x (210), x have to be bigger than y. (to correct)
 
  • #6
76
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well if its 210(degrees) counterclockwise then wouldnt the angle be 30(degrees) sin 210-180 = 30 degrees
 
  • #7
76
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14.cos 30=x . if it is 30 degree to x (210), x have to be bigger than y. (to correct)
why would x be cos and not y. if the vector is in the third quadrant and cos is adjacent/hypotenuse then adjacent would be x so the only side left would be y which you would be solving for.
 
  • #8
76
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anybody please
 
  • #9
Char. Limit
Gold Member
1,204
14
why would x be cos and not y. if the vector is in the third quadrant and cos is adjacent/hypotenuse then adjacent would be x so the only side left would be y which you would be solving for.
I'm not sure what you mean...

If you mean that the x component should correspond to the cosine, this is because the cosine of the angle measures the length of the adjacent side to the angle, in this case, the x-axis.
 
  • #10
76
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ok i got it thanks.

14cos30 = -12.1 x-component
14sin30 = -7.0 y-component
 

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