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

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SUMMARY

The discussion focuses on graphically determining the resultant of three vector displacements: 34m at 25 degrees north of east, 48m at 33 degrees east of north, and 22m at 56 degrees west of south. The resultant vector calculated is 58m at an angle of 48 degrees. Participants emphasized the importance of correctly assigning x and y components using trigonometric functions, specifically noting the need to consider the direction of each vector. Accurate graphical representation and careful attention to angle assignments are crucial for correct calculations.

PREREQUISITES
  • Understanding of vector components and displacements
  • Basic trigonometry, specifically sine and cosine functions
  • Ability to graphically represent vectors
  • Familiarity with angle measurements in degrees
NEXT STEPS
  • Practice vector addition using graphical methods
  • Learn about vector decomposition into x and y components
  • Explore the use of software tools for vector analysis
  • Study the principles of resultant vectors in physics
USEFUL FOR

Students in physics or engineering, educators teaching vector analysis, and anyone interested in mastering graphical methods for vector addition.

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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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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.
 

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