Graphically determine resultant vector displacement

[Surgikill117]

Homework Statement

Graphically determine the resultant of the following three vector displacements:
1) 24m, 30 degrees North of East
2) 28m, 37 degrees East of North
3) 20m, 50 degrees South of West

Homework Equations

The Attempt at a Solution

I have the vectors drawn but I can't figure out how to find the resultant displacement. I can't get a right triangle so I can use the Pythagorean theorem.

 

[Basic_Physics]

The resultant is the vector drawn from the tail of the first to the head of the last vectors.

 

[lewando]

If you are solving this graphically, a ruler and protractor will help.

 

[Surgikill117]

I know that but I need to have a set of coordinates to go with it, like 40 degrees North of West. The answer is in the back of the book but my teacher needs to see work. I can't figure out how I can find the angle and length.

Lewando: Everything has to be done with math. My teacher says that a ruler and protractor are not accurate enough.

 

[lewando]

Agree that solving this purely "graphically" will have some graphical error. I thought you were constrained by the question. If you are not constrained, then use the component method. As a check, your low-accuracy graphical method result should be close to your component method result.

 

[Surgikill117]

Can I ask what the component method is?

 

[lewando]

Here is a good link: http://hyperphysics.phy-astr.gsu.edu/hbase/vect.html

 

[lewando]

Maybe you are more familiar with the Law of Cosines method. This is used for adding two vectors that are not at a right angle. If you want to add three vectors using this method, add two of the vectors to find an intermediate resultant. Then use the same method to add the third vector to the intermediate resultant to get the final resultant. Here is another good link:

 

[Basic_Physics]

Did you get the resultant displacement's distance and direction graphically?