Vector questions with X and Y Components

In summary: Probably, but even so, the figure with the three paths doesn't have enough sides to be a quadrilateral.In summary, Vectors are important for understanding displacement, velocity, and angle. In part 3 of this math lesson, you were introduced to vectors and needed to understand how to calculate displacement, average velocity, and angle.
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Homework Statement
Vectors
Relevant Equations
If I walk 20 km North, then 15 km East, then 10 km at 35° South of East

1-What is the magnitude of my displacement?

2-What is the angle of my displacement from east?

3-If I travel the entire distance in 4 hours, then what is my average velocity?
I know what x and y components are but this is really confusing me. And the angle I think is the inverse of tan something. part 3 is so confusing smh
 
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  • #2
homeworks said:
Homework Statement:: Vectors
Relevant Equations:: If I walk 20 km North, then 15 km East, then 10 km at 35° South of East

1-What is the magnitude of my displacement?

2-What is the angle of my displacement from east?

3-If I travel the entire distance in 4 hours, then what is my average velocity?

I know what x and y components are but this is really confusing me. And the angle I think is the inverse of tan something. part 3 is so confusing smh
Draw the path (vector) diagram. That's ALWAYS the way to start these problems.
 
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  • #3
phinds said:
Draw the path (vector) diagram. That's ALWAYS the way to start these problems.
I have drawn it already. I did 20km N then 15 km E then 10 km at 35 S of E. I got kind of a rectangle shape but not really. idk what to do next
 
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Do you know what the words in the question mean? What is displacement? What is average velocity?
 
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vela said:
Do you know what the words in the question mean? What is displacement? What is average velocity?
Yeah displacement is the total distance in a straight line. So I would need to convert 10 km at 35 south of east to x and y component, which I guess would be x-component=10cos35 and y-component=10sin35. then what?
 
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homeworks said:
Yeah displacement is the total distance in a straight line.
Not exactly. For one thing, displacement is a vector whereas distance isn't.

Displacement is the change in position. So the question is asking you how far north and east you end up compared to where you started. Can you figure that out from your diagram?
 
  • #7
vela said:
Not exactly. For one thing, displacement is a vector whereas distance isn't.

Displacement is the change in position. So the question is asking you how far north and east you end up compared to where you started. Can you figure that out from your diagram?
No, can you?
 
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Can you answer the question if it's just the first two legs of the journey?
 
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vela said:
Can you answer the question if it's just the first two legs of the journey?
You mean if it's just 20 km North and 15 km East? Yes. it would be 25
 
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How far north and east (separately) do you end up compared to where you started?
 
  • #11
vela said:
How far north and east (separately) do you end up compared to where you started?
You end up 20 km North and 15 km East from where you started?
 
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Yup. Note that you treated walking north completely separately from walking east because the two directions are perpendicular to each other.

So now add in the last leg. How far in the northward direction does the last leg take you (negative because you'll be walking southward)? How far east does the last leg take you? Use basic trig to figure those out.
 
  • #13
Here is a drawing drawn to scale that could serve as reference for future discussion (if needed.)
In part (a) you need to find the length of OC
In part (b) you need to find angle θ.
In part (c) you need to apply the definition of average velocity. Look it up if you don't remember it, but keep in mind that it is a vector therefore you have to specify both its magnitude and direction.

Displacements.png
 
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  • #14
homeworks said:
I have drawn it already. I did 20km N then 15 km E then 10 km at 35 S of E. I got kind of a rectangle shape but not really. idk what to do next
Not a rectangle, as @kuruman's drawing in the previous post shows.
 
  • #15
Mark44 said:
Not a rectangle, as @kuruman's drawing in the previous post shows.
I think "kind of rectangle" is meant as substitute for "quadrilateral".
 
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  • #16
kuruman said:
I think "kind of rectangle" is meant as substitute for "quadrilateral".
Probably, but even so, the figure with the three paths doesn't have enough sides to be a quadrilateral.
 

Related to Vector questions with X and Y Components

1. What are vector questions with X and Y components?

Vector questions with X and Y components involve breaking down a vector into its horizontal (X) and vertical (Y) components in order to solve for its magnitude and direction.

2. How do I find the magnitude of a vector with X and Y components?

The magnitude of a vector with X and Y components can be found using the Pythagorean theorem, where the magnitude is equal to the square root of the sum of the squares of the X and Y components.

3. What is the difference between a vector's components and its magnitude?

The components of a vector refer to its horizontal (X) and vertical (Y) parts, while the magnitude refers to the overall length of the vector. In other words, the magnitude is a single value while the components are two separate values.

4. How do I find the direction of a vector with X and Y components?

The direction of a vector with X and Y components can be found using trigonometric functions. The angle can be calculated using the inverse tangent of the Y component divided by the X component.

5. Can vector questions with X and Y components be applied to real-world scenarios?

Yes, vector questions with X and Y components are commonly used in physics and engineering to solve problems involving forces, motion, and other physical quantities. They can also be applied in navigation and mapping to determine direction and distance.

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