Vector Addition: Finding Displacement Using Magnitude and Direction

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Homework Help Overview

The problem involves calculating the displacement of a car that travels 175 km west and then 80 km southwest (at a 45° angle). The original poster expresses uncertainty about how to incorporate angles into the calculation of total displacement and seeks clarification on the use of vector components.

Discussion Character

  • Exploratory, Assumption checking, Mathematical reasoning

Approaches and Questions Raised

  • Participants discuss the necessity of breaking down the vectors into x and y components to find the resultant displacement. Questions arise regarding the application of angles and the correct interpretation of vector addition.

Discussion Status

Some participants have provided guidance on using trigonometric functions to resolve the components of the vectors. However, there remains confusion about the calculations and the application of the Pythagorean theorem to find the magnitude of the resultant vector. Multiple interpretations of the problem are being explored.

Contextual Notes

Participants note that the original poster's homework may impose specific requirements or constraints that are not fully articulated in the discussion. There is also an indication of urgency regarding the completion of the task.

wadesweatt
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The Problem:
A car is driven 175 km west and then 80 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)?

I have drawn myself a diagram, and I know you need to use the angles to help decide how much displacement, but I don't know how to use them.

It seems like whenever I get the distance of each vector I can just add those two and it will give me total displacement.

How can I use the distances 175 and 80 with the angles 0 deg. and 45 deg., respectively, to find the total displacement? Is there some sort of equation I'm missing?

Thanks in advance...

Wade
 
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wadesweatt said:
The Problem:
A car is driven 175 km west and then 80 km southwest (45°). What is the displacement of the car from the point of origin (magnitude and direction)?

I have drawn myself a diagram, and I know you need to use the angles to help decide how much displacement, but I don't know how to use them.

It seems like whenever I get the distance of each vector I can just add those two and it will give me total displacement.

How can I use the distances 175 and 80 with the angles 0 deg. and 45 deg., respectively, to find the total displacement? Is there some sort of equation I'm missing?

Thanks in advance...

Wade

If you describe your vectors as x and y components the components may be added together to determine your resultant.
At that point let Pythagoras be your guide.
 
LowlyPion said:
If you describe your vectors as x and y components the components may be added together to determine your resultant.
At that point let Pythagoras be your guide.


I'm not sure I know what you mean? What is X and what is Y? and I still don't get where the angles fit in here...
 
wadesweatt said:
I'm not sure I know what you mean? What is X and what is Y? and I still don't get where the angles fit in here...

They can be whatever you want. I would choose East and North. The only real requirement is that they be orthogonal.
 
ok well I did cos (45)= (x/80) and solved for x to get 42.026. then I added that to 175 to get 217.026 for the final x-component (km). Is this correct or close? My homework says it is wrong, but I can't see why?
 
nobody?
 
wadesweatt said:
ok well I did cos (45)= (x/80) and solved for x to get 42.026. then I added that to 175 to get 217.026 for the final x-component (km). Is this correct or close? My homework says it is wrong, but I can't see why?

What about the y component?
 
well I did sin(45)=(y/80), and got 56.569. This answer is also wrong according to the computer.

Can you or anyone please explain why?
 
bump...
 
  • #10
anybody please... it's due in like 15 minutes...
 
  • #11
wadesweatt said:
well I did sin(45)=(y/80), and got 56.569. This answer is also wrong according to the computer.

Can you or anyone please explain why?

OK you have now the X- component and the Y component use the Pythagorean theorem to solve for the magnitude.

Then figure the angle from sin or cos.
 

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