Vector addition problem

  • Thread starter wadesweatt
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  • #1
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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
 

Answers and Replies

  • #2
LowlyPion
Homework Helper
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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

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
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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
LowlyPion
Homework Helper
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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
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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?
 
  • #7
LowlyPion
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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
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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?
 
  • #10
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anybody please... it's due in like 15 minutes...
 
  • #11
LowlyPion
Homework Helper
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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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