Question regarding vector diagram

[nblu]

The question was, "In a total time of 2.0 min, a duck on a pond paddles
22 m [36deg N of E] and then paddles another 65 m [25 deg E of S]"

a) Draw a vector diagram that represents this motion. Be sure to include
a scale and compass.

I understand that this is THE most basic of all, however, since this is a
independent study course from adult learning centre, I do not have anyone
whom I can ask and textbook references are limited.

Here's what I have drawn;
[img=http://img208.imageshack.us/img208/2240/cimg1695cs4.th.jpg]
(Sorry about the bad quality of the picture, I'm not good at using my cam)

 

[Midy1420]

try http://quarknet.fnal.gov/toolkits/ati/vectors.html...always try to start with a cartesian coordinate system (x and y axis)

 

[nblu]

try http://quarknet.fnal.gov/toolkits/ati/vectors.html...always try to start with a cartesian coordinate system (x and y axis)

Thanks for the link Midy.
However I still do not understand the meaning of "N of E" and "E of S" and how
it will apply to the diagram..

I'm confused between "a straight line of NorthEast" which will be a diagonal line,
or two lines drawn by going east and then north.

 

[GTrax]

You know the time for this paddling episode.
You know the distance the duck covered (albeit in two different directions).
So figure the scalar value (duck speed).

Scalar values (like duck speed) have magnitude only. They become vector values when we include the directions involved.

So now, you can make a new vector diagram, with the correct magnitude vectors. The resultant vector motion of the duck is easy to see.

The 'other' way to do this is to figure the distance to the duck final stop using trigonometry. Then divide that by the time taken, to get to the resultant duck vector. You would still then need to make the vector diagram anyway. So don't do it. Go directly for what is asked.

 

[GTrax]

First - we are assuming you know which directions are North..South..East..West when you look down on a map. if we are wrong - say so now for help on that.

Some direction (say) North of East means start off pointing to East, then turn through the angle towards North (clockwise in this case). You then draw a line from a starting point of your diagram at that angle. in fact, the way you drew it in your diagram was correct for direction. It was the length of the line that was wrong. It has to represent duck-speed.

Next, the resultant is found by adding the vectors. If you draw both pointing away from the same spot, you use a parallelogram diagram to get the resultant diagonal.

If instead, you draw one vector (length and direction), then from the tip point of that, draw the other (magnitude and direction), then the resultant (complete the triangle) is a vector from where you started to where you finished. Its the same as the parallelogram diagonal.

 

[nblu]

First - we are assuming you know which directions are North..South..East..West when you look down on a map. if we are wrong - say so now for help on that.

Some direction (say) North of East means start off pointing to East, then turn through the angle towards North (clockwise in this case). You then draw a line from a starting point of your diagram at that angle. in fact, the way you drew it in your diagram was correct for direction. It was the length of the line that was wrong. It has to represent duck-speed.

Next, the resultant is found by adding the vectors. If you draw both pointing away from the same spot, you use a parallelogram diagram to get the resultant diagonal.

If instead, you draw one vector (length and direction), then from the tip point of that, draw the other (magnitude and direction), then the resultant (complete the triangle) is a vector from where you started to where you finished. Its the same as the parallelogram diagonal.

Thank you for your explanation.
I've never had any problem with vector diagrams before,
but that second vector (65m) is confusing me. I was thinking
that the second vector(25' EofS) should start from the head of the first vector
and it should meet(or end at) the horizontal axis, but then the distance wouldn't
make any sense..

 

[nblu]

Is this right?
also since this is not a right-angle triangle
how do i calculate the resultant vector? or the total displacement.
http://img208.imageshack.us/img208/4216/vectoreu9.jpg

 

[GTrax]

The 36 degrees N of East looks about right in your diagram, but the 25 E of S looks wrong.
25 E of S means, at the tip of the first vector "Start by facing South, and turn 25 degrees (anticlockwise) towards the East".