Vector Addition: Finding Displacement Using Magnitude and Direction

In summary: If it does then you have found your displacement. If it doesn't then there is likely an error in your original calculation and you will need to check your work. 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. 45 and see if that matches the angle on the diagram. If it does then you have found your displacement. If it doesn't then there is likely an error in your original calculation and you will need to check your work.
  • #1
wadesweatt
33
0
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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  • #2
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.
 
  • #3
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...
 
  • #4
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.
 
  • #5
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?
 
  • #6
nobody?
 
  • #7
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?
 
  • #8
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?
 
  • #9
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.
 

Related to Vector Addition: Finding Displacement Using Magnitude and Direction

What is a vector addition problem?

A vector addition problem involves adding two or more vectors together to find the resultant vector. Vectors are quantities that have both magnitude and direction, and can be represented by arrows.

How do you add vectors?

To add vectors, you must first make sure they are in the same dimension (2D or 3D). Then, you add the corresponding components of each vector. For example, to add two 2D vectors, you would add their x-components and y-components separately.

What is the difference between vector addition and scalar addition?

Vector addition involves adding two or more vectors together, while scalar addition involves adding two or more scalar quantities together. Scalar quantities only have magnitude, while vectors have magnitude and direction.

What is the commutative property of vector addition?

The commutative property of vector addition states that the order in which vectors are added does not matter. In other words, adding vector A to vector B will give the same result as adding vector B to vector A.

How do you find the magnitude and direction of the resultant vector in a vector addition problem?

The magnitude of the resultant vector can be found using the Pythagorean theorem (c = sqrt(a^2 + b^2)) and the direction can be found using trigonometric functions such as tangent (tan). Alternatively, you can use the law of cosines to find the magnitude and direction of the resultant vector.

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