What is the resultant displacement of the newspaper delivery route?

[ashonte]

Homework Statement

a girl delivering newspaper covers her route by traveling 4 blocks west, 2 blocks north, the 9 blocks east. what is her resultant displacement?

Homework Equations

do i even begin at solving this?

The Attempt at a Solution

i have no idea how to do this

 

[lewando]

Are need to be familiar with adding displacement vectors. Do you have a textbook with a similar example?

 

[ashonte]

no i do not have a textbook example

 

[lewando]

There are lots of googleable references available such as:
http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

Let me know if this is helpful.

 

[lewando]

While you are researching this topic...some more thoughts:
1. Assume that a "block" is a acceptable unit of linear distance measurement for the sake of this problem.
2. Draw a pictue that maps out her walk onto an x-y coordinate system. A common convention is to associate East with the +x direction and North with the +y direction. Also, for simplicity, have her start out at the origin (x,y) = (0,0).
3. When people talk about a "resultant displacement" what they are really after are two things: the straight-line distance between the startpoint and the endpoint and a direction (from the startpoint to the endpont).
4. Without an example, we are at a loss to understand the expected format of the answer so here are some possible answer formats:

"5 miles in the direction of east" (or northeast north-northeast--only useful if the direction angle is 90, 45, or 45/2 degrees, etc).

"6 inches at a heading of 10-degrees" (where 0-degrees is North, 90-degrees is East, etc.)

"3i + 8j millimeters", where "i" and "j" represent unit vectors in the +x and +y directions, respectively. This is cool because you don't need trigonometry to get a direction angle.

 

[ashonte]

okay so i went and looked at the website and it helped some. but when i draw my picture would i go left 4 units then up 2 and over 9 or would i plot each seperate.

 

[ashonte]

im just plain confused here :( sorry

 

[Lancelot59]

If you're doing it graphically, the method is called putting the vectors "tip to tail".

Actually draw each one out on a graph, with the tip of each vector touching the tail of the first one.

 

[lewando]

Don't be sorry. We are here to help. Ask all the questions you like--no matter how confused they sound. We'll take them one-at-a-time, and I know you will eventually "get it".

 

[ashonte]

okay i will. okay so what do i need to do

 

[Lancelot59]

He's right, not understanding something is nothing to be sorry for. You'll eventually get it, even if you develop a few grey hairs along the way.

I said further up, just do basic vector addition, place the vectors on a graph tip to tail.

I'll explain this in the form of an analogy, say you have a list of steps you need to make in a dance. Each one of those could be the vectors.

Take 4 steps to the left
Take 2 steps forward
Take 9 steps to the right

The purpose of this 'dance' is to move you to a spot on the floor, in this case the resulting location will have a table with a fancy top hat on it. Each step moves you over a certain number of steps at a time in a certain direction.

Now imagine you made arrows for each of the dances steps. So you made one that was the same length as 4 steps, one that was 2 steps long, and one that was 9 steps long.

To plan where you want the fancy table with the top hat to go, you need to know where you're going to end up right?

Well you have a bunch of arrows, each of which has a length that equals the distance covered in each step respectively.

So all you have to do is lay the arrows down in order, in the proper directions. So put the first one facing left from your starting position. Then place the second arrow at the end of the first, facing forward, etc.

Then you have a bunch of arrows which zig zag their way to the spot you'll end up, and you now know where to place your stylish new hat.

Picture that for a bit. If you get the idea keep reading.

Now let's put this in context of vectors on a graph. The number of 'steps' in the analogy above is what we call a magnitude. It doesn't have any direction, it's just a plain scalar value. It just means the amount of something. That's just saying the arrow is however many steps long. In order for it to be a vector it must have a direction as well.

That's where the north, south, east, west directions come in. They define what direction the vector points. That's how we were able to properly place the arrows in the analogy above.

So in order to figure out where you're going to end up, place back end of the first "arrow" on your starting location, (position 0,0). Then place the back end of the next vector on the tip of the one before it facing the right direction, and so on.

When you finish placing all these vectors (the arrows) tip to tail in the right orientation and order, the final arrow will point to the resulting location.

Do you understand the idea now?