Final Displacement of 4.5 km SE, 3 km E, 6 km N & 30° NW

[kyleharvey7]

Say someone travels 4.5 km southeast, 3 km east, 6 km north and 30 degrees north of west, what is their final displacement?

 

[Quaoar]

Convert each to their x and y components...for instance, 4.5 SE would become (4.5 / sqrt(2)) * i - (4.5 / sqrt(2)) * j. Once you have all the i's and j's, add them all together, and then use the pythagorean theorem to find out the length of the vector.

 

[Gokul43201]

Say someone travels 4.5 km southeast, 3 km east, 6 km north and 30 degrees north of west, what is their final displacement?

What do you think about it ? (read our posting guidelines)

Next time, post such questions under the relevant Homework & Coursework subforum

 

[kyleharvey7]

I don't think I understand that fully. Like I understand that when finding for a triangle vector you squareroot your distances then square your product to find the resultant displacement. But I'm not sure I follow your equation

 

[Gokul43201]

kyle, what have you attempted so far, towards solving this problem ?

 

[kyleharvey7]

To tell you the truth, I am stumped. I've drawn the diagram and I'm not sure I understand the 30 degrees north of west part. I'm only in grade 10 so I almost need you to explain how to do this.

 

[FrogPad]

Try walking it yourself and then measure from your beginning destination.

You should probably let km = meters or maybe feet for ease on your legs.

Or instead you could show a little work and someone would be very helpful with you.

Or you could setup a coordinate system and assign vectors to each of displacements.

 

[Gokul43201]

Okay, the diagram is always a good place to start.

But you must also have learned how to decompose/project vectors along a pair of perpendicular axes. Given some general vector in the x-y plane, can you find its x-component and y-component ?

 

[kyleharvey7]

No, we did not. The work was taken up much differently then the way you are saying it, and the example i have from my tutor is a much different question. So for all numbers I have labelled it as so. Also, my scale is 1cm equals 1 km. So I have; Delta D1= 4.5cm Delta D2= 3cm Delta D4= 6cm and from that point I have drawn 30 degrees west of north.

 

[Gokul43201]

Are you asked to solve this problem using a scale drawing ? Or using vector math ?

Can you write down the complete question exactly as it appears in your textbook/homework/etc ?

 

[kyleharvey7]

It is not as much the problem that I don't understand because I have it drawn correctly. From my last point, the resultant vector is 30 degrees, how do you find the displacement from that point, to my beginning point?

 

[Gokul43201]

It is not as much the problem that I don't understand because I have it drawn correctly.

You may understand the question, but unless you write it down completely, I can't understand it. There are different ways to solve the problem and I don't know which way you're supposed to do it.

From my last point, the resultant vector is 30 degrees, how do you find the displacement from that point, to my beginning point?

Have you drawn all the vectors, including this last one ?

If you've drawn all the individual vectors and attached them head to tail, then your total displacement vector, which is the sum of all these vectors, is simply the line drawn from the first tail to the last head.

 

[kyleharvey7]

Eek, I wish I could show you what I have drawn because I do not know how to explain what I have done.

 

[Gokul43201]

You can attach images using the "manage attachments" option in the "go advanced" mode.

If you've drawn something on paper, can you describe it in detail ? If this is on square (graphing) paper, perhaps you can tell the coordinates of the ends of each arrow ?

 

[kyleharvey7]

Says that it is too big

 

[Gokul43201]

How did you draw it ? On Windows you can just make a simple sketch in Paint (keep the size of the workspace to less than say 200 X 150 pixels) , save it as JPEG and attach it. If you save it as a BMP, it may exceed the filesize limit.

 

[kyleharvey7]

k that might be my problem

 

[Gokul43201]

I should have noticed this earlier - and I apologize for not doing so - but there's a mistake in the question. It does not tell you the distance traveled in the last leg; only the direction. The question is incomplete.

As for the figure above, you'd want to calculate what A and B are. First notice that ABD1 is an isoceles triangle, with A=B. Since you know D1, you can calculate A (and hence B) using the Pythgoras theorem. As for the last bit (D4), there is not enough information in the question.

OR...you haven't written down the question correctly!