How Do You Graphically Determine the Resultant of Three Vector Displacements?

In summary, we need to determine the resultant of three vector displacements: (1) 34m, 25 degrees north of east; (2) 48m, 33 degrees east of north; and (3) 22m, 56 degrees west of south. Using the equations Vr=V1+V2+V3, x=mag x cos of angle, and y=mag x sin of angle, the resultant is found to be 58m, 48 degrees. However, careful attention must be paid to correctly assign lengths to x,y coordinates and to consider negative displacements when drawing the vectors on paper.
  • #1
High_Voltage
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Homework Statement


Graphically determine the resultant of the following three vector displacements: (1) 34m, 25 degrees north of east;(2) 48m, 33 degrees east of north; and (3) 22m, 56 degrees west of south.


Homework Equations


Vr=V1+V2+V3
x=mag x cos of angle
y=mag x sin of angle

The answer is 58m,48 degrees

The Attempt at a Solution



I have tried everything and I cannot put it all but here is what I got:

34,25= (x=30.8 y=14.36)
22,56= (x=12.30 y18.23)
48,33= (x=40.25 y=26.14)
 
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  • #2
You have incorrectly assigned lengths to x,y coordinates in some cases. Be careful about which angle is given when using sin/cos to calculate legs of the triangle (basic trigonometry says 'Hello'). And draw all these vectors on paper - as they vectors, some displacements will be negative.
 

FAQ: How Do You Graphically Determine the Resultant of Three Vector Displacements?

1. How do you use vector addition to "desperate" objects?

Vector addition is a mathematical operation used to combine two or more vectors to create a new vector. In the context of "desperating" objects, vector addition can be used to determine the resultant force or displacement of multiple forces acting on an object.

2. What is the purpose of "desperating" with vector addition?

The purpose of "desperating" with vector addition is to calculate the net effect of multiple vectors acting on an object. This can be useful in situations where an object is experiencing multiple forces or displacements at the same time.

3. Can vector addition be used with non-linear objects?

Yes, vector addition can be used with non-linear objects as long as the vectors being added are in the same plane. For three-dimensional objects, vector addition can be used in the x, y, and z directions to determine the resultant force or displacement.

4. Are there any limitations to using vector addition for "desperating" objects?

One limitation of using vector addition for "desperating" objects is that it only takes into account the magnitude and direction of the vectors, not their points of application. This means that the calculated resultant force or displacement may not be entirely accurate in real-world scenarios.

5. How can vector addition be applied to real-world situations?

Vector addition can be applied to various real-world situations, such as calculating the net force acting on a moving object or determining the direction and magnitude of a resultant force in a system. It is commonly used in physics, engineering, and other fields to solve complex problems involving multiple forces or displacements.

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