Vector questions with X and Y Components

  • Thread starter Thread starter homeworks
  • Start date Start date
  • Tags Tags
    Components Vector
Click For Summary
SUMMARY

This discussion centers on solving vector problems involving displacement and average velocity. The user describes a journey consisting of 20 km North, 15 km East, and 10 km at 35° South of East, seeking to determine the magnitude of displacement, the angle from east, and average velocity. Key insights include the necessity of converting the final leg of the journey into x and y components using trigonometric functions, specifically cosine and sine, to accurately calculate displacement. The importance of understanding displacement as a vector quantity, distinct from distance, is emphasized throughout the conversation.

PREREQUISITES
  • Understanding of vector components and their representation
  • Knowledge of trigonometric functions, specifically sine and cosine
  • Familiarity with the concept of displacement versus distance
  • Basic understanding of average velocity as a vector quantity
NEXT STEPS
  • Learn how to calculate vector displacement using trigonometric identities
  • Study the concept of average velocity and its vector nature
  • Explore graphical methods for vector addition and representation
  • Practice solving similar vector problems using different angles and distances
USEFUL FOR

Students studying physics, particularly those focusing on mechanics and vector analysis, as well as educators seeking to clarify concepts of displacement and average velocity in a practical context.

homeworks
Messages
6
Reaction score
0
Member warned that homework posts must include an attempt.
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
 
Physics news on Phys.org
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.
 
  • Like
Likes   Reactions: Hall
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
 
Do you know what the words in the question mean? What is displacement? What is average velocity?
 
  • Like
Likes   Reactions: PeroK
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?
 
  • Sad
Likes   Reactions: PeroK
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?
 
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?
 
  • Sad
Likes   Reactions: PeroK
Can you answer the question if it's just the first two legs of the journey?
 
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
 
  • #10
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?
 
  • #12
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
 
  • Like
Likes   Reactions: jbriggs444, Steve4Physics and Hall
  • #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".
 
  • Like
Likes   Reactions: PeroK
  • #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.
 

Similar threads

Understanding Forces and their Vector Components
  • · Replies 8 ·
Replies
8
Views
783
Can A Vector Have Components Of Say Y or Z in the X-Hat Direction?
  • · Replies 8 ·
Replies
8
Views
1K
Calculate electric force using Coulomb's law (vector components are the struggle)
  • · Replies 3 ·
Replies
3
Views
1K
Question about vector components
  • · Replies 5 ·
Replies
5
Views
2K
Am I Calculating the Components of V3 Correctly?
  • · Replies 9 ·
Replies
9
Views
2K
Confusion with force components
  • · Replies 21 ·
Replies
21
Views
3K
Diffrence between resolving vector to components and find projections
  • · Replies 4 ·
Replies
4
Views
1K
Two dimensional motion problem (kicking a soccer ball into the goal)
  • · Replies 3 ·
Replies
3
Views
991
I want to know if the sketch I've drawn of the catenary suits the exercise
  • · Replies 11 ·
Replies
11
Views
1K
Calculating Vector Components with given Magnitude and Direction
  • · Replies 11 ·
Replies
11
Views
2K