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?

LowlyPion
Homework Helper
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?

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.

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
Homework Helper
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?

LowlyPion
Homework Helper
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?

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...

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

LowlyPion
Homework Helper
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.