Vector Addition and Components

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In summary, the conversation is about a problem where the (a)x and (b)y components of a vector need to be calculated in order for the sum of four vectors to be zero. The vectors are given in units, with the +x direction being due east and the +y direction being due north. The individual components of each vector are calculated and the answer is found to be 270 units, but this is not the correct answer in terms of significant digits. The conversation then shifts to discussing how to properly calculate the components, with one person mentioning the need to choose a direction to call 0° and express the angles with respect to that reference. The conversation ends with a discussion about the number of significant digits in the answer.
  • #1
zn23
18
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ok i need help with this type of question

What are the (a)x and (b)y components of the vector that must be added to the following three vectors, so that the sum of the four vectors is zero? Due east is the +x direction, and due north is the +y direction.

A= 141 units, 59.0 ° south of west
B= 243 units, 38.0 ° south of east
C= 173 units, 29.0 ° north of east

a)=___________
b)=___________

i tried finding the x components by simple multiplying the units by cos(angle), found my answer to be 270 units which i know is wrong.

I have a feelin that yur supposed go x=sin n y=cos in some vectors but I am not 100% sure
 
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  • #2
Very Tough Kinematics 1 dimension problem

Homework Statement



What are the (a)x and (b)y components of the vector that must be added to the following three vectors, so that the sum of the four vectors is zero? Due east is the +x direction, and due north is the +y direction.

A= 141 units, 59.0 ° south of west
B= 243 units, 38.0 ° south of east
C= 173 units, 29.0 ° north of east

a)=___________
b)=___________

Answer must be in 3 significant digits

Homework Equations





The Attempt at a Solution



The answer is not a):270 or b) -204.95 I've tried n its wrong...

so please if u can help out than great
 
  • #3


Well the first thing i would do is decompose each of the given vectors into their x and y components. Is that how you did it? How exactly did you get the answers you came up with?
 
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  • #4


danago said:
Well the first thing i would do is decompose each of the given vectors into their x and y components. Is that how you did it?

thats exactly how i started

A= x: 173cos29=151.30
y: 173sin29= 83.87

B= x: 243cos38=191.48
y: 243sin38= 149.60

C= x: 141cos59= 72.62
y: 141sin59= 138.35

when i looked for the displacement of x i got 270.16, and to signifiant digits i can't get 3 out of that because the answer equires 3
for y the total displacement : was -204.08 and that was wrong as well...

I don't know i think this is one of those types of questions where some vectors you have to switch between x n y, like x wud be sin and y wud be cos, but i just don't know when and how to do that in the question...
 
  • #5


zn23 said:
thats exactly how i started

A= x: 173cos29=151.30
y: 173sin29= 83.87

B= x: 243cos38=191.48
y: 243sin38= 149.60

C= x: 141cos59= 72.62
y: 141sin59= 138.35

when i looked for the displacement of x i got 270.16, and to signifiant digits i can't get 3 out of that because the answer equires 3
for y the total displacement : was -204.08 and that was wrong as well...

I don't know i think this is one of those types of questions where some vectors you have to switch between x n y, like x wud be sin and y wud be cos, but i just don't know when and how to do that in the question...

If you add 270 to 270 do you really get zero?:wink:
 
  • #6


Something you seem to have overlooked is the positive and negative signs on some of your components. It often makes it easier to draw each vector in the x-y plane first.

Looking at vector B, for example. 243 units, 38.0 ° south of east. If you draw that, it will look like a vector with a length of 243 units, and it will point in a direction of 38 degrees below the positive x axis. Now think about each of its components; Its x component points in the +x direction so it will be positive, but the y component is in the -y direction and so it will be negative,
 
  • #7


^^^ i actually have done, although i didnt display it,

for total x value : A + B - C , C is the only one in the west direction therefore I had to subtract it

(151.30) + (191.48)- (72.62) = 270. 15

i did the same for y but its the wrong answer...
 
  • #8


zn23 said:
^^^ i actually have done, although i didnt display it,

for total x value : A + B - C

(151.30) + (191.48)- (72.62) = 270. 15

i did the same for y but its the wrong answer...

The original question ask you which vector you have to add to this total in order to get zero...if you add 270 to 270 do you get zero?:wink:
 
  • #9
zn23 said:
A= 141 units, 59.0 ° south of west
B= 243 units, 38.0 ° south of east
C= 173 units, 29.0 ° north of east

Choose a direction to call 0°, and express the angles with respect to that reference.

[edit: look at the problem statement for clues as to where 0 and 90 should point]

Regards,

Bill
 
Last edited:
  • #10
Antenna Guy said:
Choose a direction to call 0°, and express the angles with respect to that reference.

Regards,

Bill

? come again? lol sorry i misunderstand
 
  • #11


^^ yea if the answer was 270 and i add (-270) that will become 0, only problem is i have to display the answer in 3 significant digits, and -270 is only 2 significant digits...
 
  • #12


zn23 said:
^^ yea if the answer was 270 and i add (-270) that will become 0, only problem is i have to display the answer in 3 significant digits, and -270 is only 2 significant digits...

-270 is 3 sig digs
 
  • #13


gabbagabbahey said:
-270 is 3 sig digs

i believe its 2, becuz if u were to put it into scientific notation it wud 27 x 10 ^ 1 or 2.7 X 10 ^ 2. A Trailing 0 is only significant if its after a decimal point, 27.0 wud be 3, but that's not the answer
 
  • #14


zn23 said:
i believe its 2, becuz if u were to put it into scientific notation it wud 27 x 10 ^ 1 or 2.7 X 10 ^ 2. A Trailing 0 is only significant if its after a decimal point, 27.0 wud be 3, but that's not the answer

No, in this case the zero is significant because it was rounded from 0.1 to 0 and so you would have -2.70 X 10^2...Just because the 3rd sig fig is zero doesn't mean it isn't significant.
 
  • #15
zn23 said:
? come again? lol sorry i misunderstand

59° South of West is either 239° from East, or -121° from East.

Regards,

Bill
 
  • #16
I cannot figure this out at all, its a question on the computer so when i type in -270, it tells me, please put the correct number of significant figures and i can't display it -2.70 x 10 ^ 2, because it doesn't allow scientic notation...
 
  • #17
zn23 said:
I cannot figure this out at all, its a question on the computer so when i type in -270, it tells me, please put the correct number of significant figures and i can't display it -2.70 x 10 ^ 2, because it doesn't allow scientic notation...

That's strange, -270 should be the right answer...maybe try -269 or -271 in case the instructor accidentally rounded each component off before adding them together.

Are you sure you copied the question out exactly?
 
  • #18
im positive^^^
 
  • #19
zn23 said:
im positive^^^

Well then I recommend you talk to /email your instructor, show him your solution and ask if it is correct
 
  • #20
lol yur a genius I am an idiot^^, the answer was -269 for x and for y it was +186.59, i tried typing it in and it was correct thanks a lot man:)
 

1. What is kinematics?

Kinematics is a branch of physics that deals with the motion of objects without considering the forces that cause the motion. It involves studying the position, velocity, and acceleration of objects in motion.

2. What makes a kinematics question "tough"?

A tough kinematics question is usually one that involves multiple variables and requires the use of complex formulas and equations to solve. It may also involve real-world scenarios and require critical thinking to solve.

3. How do I approach a tough kinematics question?

The key to solving a tough kinematics question is to break it down into smaller, more manageable parts. Identify the given information, determine what is being asked, and choose the appropriate formulas and equations to solve the problem.

4. What are some common mistakes to avoid when solving a tough kinematics question?

One common mistake is using the wrong formula or equation. It is important to carefully read the question and identify which variables are given and which are being asked for. Another mistake is not paying attention to units and using the wrong units in calculations.

5. How can I improve my understanding of kinematics to better tackle tough questions?

Practice is key to improving your understanding of kinematics. Make sure to familiarize yourself with the different formulas and equations, and work through various types of kinematics problems. It can also be helpful to seek out additional resources, such as textbooks or online tutorials, to supplement your learning.

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