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

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Homework Help Overview

The discussion revolves around a vector addition problem involving two vectors with specified magnitudes and angles. The original poster expresses confusion regarding discrepancies between their calculations and the answers provided in the textbook.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the original poster's calculation of vector components and the subsequent addition of angles. Questions are raised about the appropriateness of adding 180 degrees to the angle and the implications of vector direction.

Discussion Status

Participants are actively questioning the reasoning behind the original poster's calculations, particularly the addition of 180 degrees to the angle. There is a recognition of potential errors in the component calculations, and some guidance is offered regarding the expected quadrant for the resultant vector.

Contextual Notes

There is mention of the textbook providing different answers, which may involve rounding differences. The original poster's repeated attempts to clarify their understanding indicate a struggle with the problem setup and calculations.

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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.