Why is it important to check the magnitude of vectors when adding them?

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SUMMARY

The discussion centers on the importance of checking the magnitude of vectors when performing vector addition. A participant initially calculated a resultant velocity of 23.6 m/s but later corrected this to 5.9 m/s after realizing a multiplication error with the scale of 1 m/s = 2 cm. The correct resultant vector should be expressed in m/s, not Newtons, due to a typographical error in the source material. The angle between the vectors was confirmed to be 90°, allowing the application of the Pythagorean theorem for accurate calculations.

PREREQUISITES
  • Understanding of vector addition and resultant vectors
  • Familiarity with the Pythagorean theorem
  • Knowledge of unit conversion (e.g., m/s to cm)
  • Basic principles of physics related to forces and motion
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  • Study vector addition techniques in physics
  • Learn about unit conversion methods in scientific calculations
  • Explore the application of the Pythagorean theorem in vector analysis
  • Review common typographical errors in physics textbooks and their implications
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This discussion is beneficial for physics students, educators, and anyone involved in vector analysis or motion calculations, particularly in understanding the significance of magnitude in vector addition.

ryanking93
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Homework Statement
Add the following vectors and determine the resultants (length, angle from O)
Relevant Equations
3 m/s. 45° + 5 m/s. 135°
So I've charted the equation above, and received the correct resultant 104.0° I used a scale of 1m/s = 2cm and I get 11.8cm which gives me 23.6m/s but when I look at the answer it is 104.0° / 5.83N

I have no idea why its in Newtons.
 
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Welcome! :smile:
Could you post the original text of the problem?
The value you found is not correct.
 
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Lnewqban said:
Welcome! :smile:
Could you post the original text of the problem?

Thank you. I have attached both the questions and answers I am referencing. The specific question is "C"

And my answer to the question.
 

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Typographical error.
 
OmCheeto said:
Typographical error.

Okay, Thank you. I thought I might be losing it for a minute.
 
ryanking93 said:
Thank you. I have attached both the questions and answers I am referencing. The specific question is "C"

And my answer to the question.
It is an error of the booklet, the resultant vector should be in m/s.
Note that the angle between your vectors is 90°, therefore, you could apply the Pythagorean equation and see that the result can't be 23.6 m/s.
 
Lnewqban said:
It is an error of the booklet, the resultant vector should be in m/s.
Note that the angle between your vectors is 90°, therefore, you could apply the Pythagorean equation and see that the result can't be 23.6 m/s.

Ahhhh I see now! My issue was when I ended up with 11.8cm instead of dividing by 2 I multiplied by 2. As my scale was 1m/s = 2cm. I end up with 5.9m/s.

Thanks a million for the help!
 
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ryanking93 said:
Ahhhh I see now! My issue was when I ended up with 11.8cm instead of dividing by 2 I multiplied by 2. As my scale was 1m/s = 2cm. I end up with 5.9m/s.

Thanks a million for the help!
When adding vectors, it is good to check that the result is not greater than the addition of the magnitude of each independent vector.
You are welcome. :smile:
 
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