# Vectors and car displacement

#### amazingphysics2255

Problem Statement
A car travels 110km south and 70km west
1. Draw a vector diagram to show the journey.
2. Calculate the displacement of the car.
Relevant Equations
N/A
I have drawn a arrow pointing straight down (South) 110km and an arrow off that to the right(west) 70km.

I know that the distance of the journey would be 180km. How do I go about finding the displacement?

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Fixed.

#### FactChecker

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For the displacement distance, use the Pythagorean theorem. For the displacement angle, use trig functions.

#### FactChecker

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@FactChecker can you give me a link or formula?
It sounds like you have not had algebra or trigonometry yet. I recommend that you take those first. If you have already had them, you should brush up on the basic algebra and trig. They are necessary for a lot of subjects.

#### amazingphysics2255

I know what the Pythagorean theorem is $$a^2+b^2=c^2$$

I've deleted my previous post as it was unclear. I meant how do I use this in the Pythagorean theorem?

#### FactChecker

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Good. Then you should be able to calculate the magnitude of the displacement. How about the trig and the angles?

#### FactChecker

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I meant how do I use this in the Pythagorean theorem?
Make a drawing and label the a, b, c sides and make the appropriate calculations. You must show work on homework problems before we are allowed to help.

#### amazingphysics2255

130.38 so 130.4 km? is this the displacement? angles and trig are not needed as far as I know.

#### FactChecker

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That is the magnitude of the displacement, which may be all that is expected. If no angle is expected, you can at least say South South West. If an angle is expected, you should calculate it using arctan.

#### haruspex

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That is the magnitude of the displacement, which may be all that is expected. If no angle is expected, you can at least say South South West. If an angle is expected, you should calculate it using arctan.
Yes, it's rather silly asking for displacement, which is by definition a vector, without specifying the format of the answer. It would be valid to answer "110km S, 70km W".

#### BvU

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Well,... currently it says
Problem Statement: A car travels 110km south and 70km west
...
straight down (South) 110km and an arrow off that to the right(west)
Since 'down' refers to the paper (or the screen), one would expect 'to the right' to refer to the paper (screen) also

#### jbriggs444

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Since 'down' refers to the paper (or the screen), one would expect 'to the right' to refer to the paper (screen) also
Well, the car makes a right turn and ends up moving left. Best avoid "right" and "left" entirely given that potential ambiguity.

#### PeroK

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I have drawn a arrow pointing straight down (South) 110km and an arrow off that to the right(west) 70km.
I thought East was to the right: "Never Eat Shredded Wheat" is how I remember it, going clockwise from North.

#### FactChecker

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Well, the car makes a right turn and ends up moving left. Best avoid "right" and "left" entirely given that potential ambiguity.
They use the terms port and starboard on a boat to avoid ambiguity. They refer to left and right when facing forward.

#### BvU

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They use the terms port and starboard on a boat to avoid ambiguity
Yeah, and then they have a brass plaque 'Starboard is to the right' nailed to the mast

#### jbriggs444

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Yeah, and then they have a brass plaque 'Starboard is to the right' nailed to the mast
A good sailor always has some Red Port Left.

BvU

#### amazingphysics2255

Ok. So just south 110km and west 70km. Anything else I should know?

#### PeroK

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Ok. So just south 110km and west 70km. Anything else I should know?
Do you understand the point that @haruspex is making? Have you come across the $\vec{i}, \vec j, \vec k$ vectors yet?

#### amazingphysics2255

No, I haven't come across this as of yet. And the post by haruspex that says you can write your answer as 110km S and 70km W?

#### jbriggs444

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No, I haven't come across this as of yet. And the post by haruspex that says you can write your answer as 110km S and 70km W?
I took the response from @haruspex more as a criticism of the question than as a free pass to avoid using the Pythagorean theorem.

#### amazingphysics2255

Yeah! 130.4km . I see what he means technically your displacement would just be 110km S and 70kmW

#### PeroK

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I took the response from @haruspex more as a criticism of the question than as a free pass to avoid using the Pythagorean theorem.
I thought it was more like a legitimate option to give the displacement in Cartesian rather than polar coordinates. With NESW as the unit vectors.

#### haruspex

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Yeah! 130.4km . I see what he means technically your displacement would just be 110km S and 70kmW
I'm saying that it is a technically valid way of stating the displacement. It can also be specified in $\hat i, \hat j, \hat k$ vectors or as a magnitude and a direction. The question should have made it clear a) whether only the magnitude is required or b) if the vector is required, in what form.
If we rule out the options which make the answer too easy, that leaves either just the magnitude or the magnitude and direction. To be on the safe side, you should assume the last.

#### amazingphysics2255

Can someone draw a vector diagram so I can visualize this also? Note, the question doesn't ask for one to be drawn ( I added it to the question too, wasn't in the original question given to me). I have one on paper but don't know how to draw one on this site(can you?). Mine looks like a right-angled triangle. with the hypotenuse being 130.4km, the adjacent is 110km and the opposite is 70km.

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