Vector Addition: Finding Displacement Using Magnitude and Direction

[wadesweatt]

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

 

[LowlyPion]

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.

 

[wadesweatt]

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...

 

[LowlyPion]

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.

 

[wadesweatt]

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?

 

[wadesweatt]

nobody?

 

[LowlyPion]

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?

 

[wadesweatt]

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?

 

[wadesweatt]

bump...

 

[wadesweatt]

anybody please... it's due in like 15 minutes...

 

[LowlyPion]

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.