Addition of vectors and direction

In summary, the problem involves finding the magnitude and direction of vector C, which is the result of adding vector A and B using the component method. The magnitude of vector C is 106.5m and the direction is 16.5° counterclockwise from the positive x-axis. The calculations involve using trigonometric functions and following certain syntax requirements in order to get the correct answer.
  • #1
almangar
3
0

Homework Statement



A vector A has a magnitude of 56.0 m and points in a direction 20.0° below the positive x axis. A second vector, B, has a magnitude of 70.0 m and points in a direction 45.0° above the positive x axis.

Using the component method of vector addition, find the magnitude and direction of the vector C (counterclockwise from the positive x-axis).


Homework Equations



a) Cx = Ax + Bx
b) Cy = Ay + By
c) Ax = ACos[tex]\Theta[/tex]
d) Ay = ASin[tex]\Theta[/tex]
e) Bx = BCos[tex]\Theta[/tex]
f) By = BSin[tex]\Theta[/tex]

The Attempt at a Solution



I have calculated out all the relevant equations:
a) Cx = 52.6 + 49.5 = 102.1m
b) Cy = 49.5 - 19.2 = 30.3m
c) Ax = 56Cos20 = 52.6m
d) Ay = 56Sin20 = -19.2m (negative due to y in the negative direction per my written graph)
e) Bx = 70Cos45 = 49.5m
f) By = 70Sin45 = 49.5m

I have come up with vector C to be 106.5m using the Pythagorean theorem, but I cannot seem to get the correct direction of vector C. I have tried using the equation tan[tex]^{-1}[/tex](Cy/Cx) which gives me tan[tex]^{-1}[/tex](30.3/102.1) = 16.5, but when I plug it into the answer it tells me to check my syntax. By my graph, Vector C is in Q1 so I would assume from x-axis counter clockwise the answer should be 16.5deg. What I am unsure of is the fact that Vector A is in QIV and therefore the angle is intersected by the x-axis, so maybe that is where I am having my problem. My professor didn't really cover anything to this degree, so I have been relying on the book and it hasn't been much help either. Your help is greatly appreciated.

As this is my first post to this forum, I was trying to follow the rules to the letter, but if I don't need to type everything I did, would someone please let me know. Thank you very much.

Ahhh...The joy of returning to school after a 10 year hiatus!
 
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  • #2
Your answer looks fine to me, so it must be that the automated system you are plugging it into requires it to be in a certain form (syntax).
 
  • #3
What other form could there be. It is asking for the direction counterclockwise from the x-axis and is asking for the answer in degrees.
 
  • #4
Nevermind, I was racking my brain to try and figure out what the problem was, so I just decided to forget it and try re-inputting my answer again after about 4 different times of working out the problem and it finally took my answer @ 16.5 deg which is what I had put into the automated system originally. Thanks for your help.
 

What is the definition of vector addition?

Vector addition is the process of combining two or more vectors to create a new vector that represents the resultant magnitude and direction of the original vectors.

How do you add vectors using the graphical method?

To add vectors using the graphical method, you must draw the two vectors on a coordinate plane and then use the parallelogram rule to find the resultant vector. The resultant vector is drawn from the tail of the first vector to the head of the second vector.

What is the difference between vector addition and scalar addition?

Vector addition involves combining vectors that have both magnitude and direction, while scalar addition involves adding quantities that only have magnitude.

Can vectors be added in any order?

Yes, vectors can be added in any order using the commutative property of addition. This means that the order in which the vectors are added does not affect the final result.

What is the importance of considering direction in vector addition?

Direction is important in vector addition because it determines the final direction of the resultant vector. Without considering direction, the final result may be inaccurate or misleading.

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