Why Do My Vector Addition Calculations Differ from the Textbook's Answers?

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SUMMARY

The discussion centers on vector addition calculations involving two vectors, A and B, with magnitudes and angles provided. The user initially miscalculates the components of vector B, leading to an incorrect resultant vector and angle. The correct answers from the textbook are R=27.27 and θ=33.14, which the user later realizes are due to rounding differences. Key insights include the importance of correctly identifying vector quadrants and avoiding unnecessary angle adjustments.

PREREQUISITES
  • Understanding of vector components and trigonometric functions
  • Familiarity with the Pythagorean theorem
  • Knowledge of angle measurement in degrees
  • Ability to interpret vector direction and quadrant placement
NEXT STEPS
  • Review vector addition techniques using trigonometric functions
  • Study the Pythagorean theorem applications in physics
  • Learn about vector quadrant analysis and its implications
  • Explore rounding techniques in mathematical calculations
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry, as well as educators seeking to clarify common misconceptions in vector addition.

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Homework Statement



Hi, for some reason I can't post my homework question (Grade 12 math)


How do i fix this?

Here's my homework question






Homework Statement



In Exercises 15-30, add the given vectors by using the trigonometric functions and the Pythagorean theorem

19. A = 9.821,θA = 34.27
B = 17.45,θB = 752.50

Homework Equations



R=√Rx2+Ry2=

θ=tan-1 Ry/Rx =

The Attempt at a Solution




So here's what I did. I copied exactly what my teacher did but, when I checked the answer at the back of the book, the answer was wrong =(. Can you guys point out how I'm not getting the correct answer? thanks.


Here's what I have so far

19.

x component y component

Ax= 9.821cos34.27 Ay=9.821sin34.27
= 8.116 =5.530

Bx=17.45cos752.50 By=17.45cos752.50
= 14.72 =14.72



=22.84 =20.25

R=√22.84(2) + 20.25(2)= 30.52


θ=tan-1 20.25/22.84=41.56

θ=180+41.56




EDIT IT SAYS IN THE BOOK THAT THE ANSWERS ARE

R=27.27, θ=33.14
 
Last edited:
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Why have you added 180 degrees to your angle?

Note that BOTH of your vectors lie in the first quadrant, so their sum must lie there as well.
 
arildno said:
Why have you added 180 degrees to your angle?

Note that BOTH of your vectors lie in the first quadrant, so their sum must lie there as well.

?

I don't get it =(
 
Last chance U said:
?

I don't get it =(

Both of your given vectors point to the northeast, so their sum must also point to the northeast. When you added 180 degrees to the angle you forced your vector to point to the southwest. Why would you do that?
 
Last chance U said:

Homework Statement



Hi, for some reason I can't post my homework question (Grade 12 math)


How do i fix this?

Here's my homework question






Homework Statement



In Exercises 15-30, add the given vectors by using the trigonometric functions and the Pythagorean theorem

19. A = 9.821,θA = 34.27
B = 17.45,θB = 752.50

Homework Equations



R=√Rx2+Ry2=

θ=tan-1 Ry/Rx =

The Attempt at a Solution




So here's what I did. I copied exactly what my teacher did but, when I checked the answer at the back of the book, the answer was wrong =(. Can you guys point out how I'm not getting the correct answer? thanks.


Here's what I have so far

19.

x component y component

Ax= 9.821cos34.27 Ay=9.821sin34.27
= 8.116 =5.530

Bx=17.45cos752.50 By=17.45cos752.50
= 14.72 =14.72
Your components for ##\vec{B}## are wrong. They shouldn't be equal.

=22.84 =20.25

R=√22.84(2) + 20.25(2)= 30.52


θ=tan-1 20.25/22.84=41.56

θ=180+41.56
Even with your incorrect numbers, both components of ##\vec{R}## are positive, so you should expect the angle to be between 0° and 90°, which is what you got from the arctangent function. So why did you add 180° to your result?

EDIT IT SAYS IN THE BOOK THAT THE ANSWERS ARE

R=27.27, θ=33.14
 
Update guys, I have actually had the right the answer the whole time rofl. The book just rounded it differently lol. Thanks for the help though.