# Difference between distance in physics and math

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1. Sep 9, 2016

### Arif Setiawan

Hai guys.. Today I've some discussion with math teacher. He wrote a question for his student about displacement. (Somehow A boat go to west 3 km, then move to north 4km. How is distance between A to the end?)
In my opinion, that question better stated as "How is displacement". But in math perspective he said that shortest path is distance. Anybody can make this clear or giving some clues?
Thanks before

2. Sep 9, 2016

3. Sep 9, 2016

### Staff: Mentor

If he wanted to ask a question to which the correct answer is "5 km", then he could not ask for "the displacement" because the only correct answer to that involves both a magnitude and a direction. He could ask for "the magnitude of the displacement from A" but that is exactly the same as asking for the distance of the end point from A.

a "distance" measure between two points always implies a straight-line measure, unless otherwise indicated

4. Sep 9, 2016

### Arif Setiawan

I get your point. In math, expected answer just magnitude. So, I think better term is "distance" as like my math teacher said. Thanks in advance

5. Sep 9, 2016

### DarkBabylon

I don't think he'd be mentioning directions if it were just the distance traveled, so I think he means the distance between point A to the end point. That's the usual format of the questions, otherwise they would have asked "what is the distanced traveled" in which the answer doesn't require much.
What you should do is ask the teacher to clarify the language they use. What do they mean about distance for example.
Usually the accepted terminology is this:
Distance - difference between point A and B.
Displacement - difference between point A and B and angle (if not told in respect to something, specify an axis you measure the angle from)
Distance traveled - the real distance in the route, not the shortest.

6. Sep 9, 2016

### my2cts

Let's make this a little more interesting.
Since the displacement occurs on a sphere, Pythagoras' theorem, C^2=A^2+B^2, must not be used.
Instead, cos(C/R) = cos(A/R) cos(B/R) with R the radius of Earth. Thus C=4.99999987 km.
1 thickness of a hair less than 5 km. :-)