Graphically determine resultant vector displacement

In summary, the problem asks for the resultant of three vector displacements: 24m, 30 degrees North of East, 28m, 37 degrees East of North, and 20m, 50 degrees South of West. The solution can be found using the component method or the Law of Cosines method. The former involves adding the components of each vector in the x and y direction, while the latter involves adding two vectors at a time using the Law of Cosines formula. A graphical method can also be used, but may have some error.
  • #1
Surgikill117
12
0

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.
 
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  • #2
The resultant is the vector drawn from the tail of the first to the head of the last vectors.
 
  • #3
If you are solving this graphically, a ruler and protractor will help.
 
  • #4
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.
 
  • #5
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.
 
  • #6
Can I ask what the component method is?
 
  • #8
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:
 
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  • #9
Did you get the resultant displacement's distance and direction graphically?
 

1. What is a resultant vector displacement?

A resultant vector displacement is the overall displacement or distance traveled by an object, taking into account both magnitude and direction. It is the combination of two or more individual vectors.

2. How do you determine the resultant vector displacement graphically?

To determine the resultant vector displacement graphically, you must first draw a scaled vector diagram for each individual vector. Then, you can use the head-to-tail method to add the vectors together, placing the tail of each vector at the head of the previous one. The resulting vector from the initial tail to final head represents the resultant vector displacement.

3. What is the importance of determining resultant vector displacement?

Determining resultant vector displacement is important because it allows us to accurately represent and analyze the motion of objects in multiple directions. It is also essential in fields such as engineering, physics, and navigation.

4. Can the resultant vector displacement be negative?

Yes, the resultant vector displacement can be negative. A negative displacement indicates that the object has moved in the opposite direction of the reference point. This can occur when vectors with opposite directions cancel each other out.

5. What factors can affect the accuracy of graphically determining resultant vector displacement?

The accuracy of graphically determining resultant vector displacement can be affected by factors such as the scale of the vector diagram, the precision of the measurements, and human error in drawing and adding the vectors. It is important to use a large enough scale and to be careful and precise in order to obtain an accurate result.

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