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

[Last chance U]

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

 

[arildno]

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.

 

[Last chance U]

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 =(

 

[Ray Vickson]

?

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?

 

[vela]

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

 

[Last chance U]

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.