Vector Addition: Finding Displacement

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SUMMARY

The discussion focuses on calculating the displacement of the Smith family's vacation route involving vector addition. The initial calculations of the X and Y components were incorrect, particularly for the 294 km southwest vector, which should be calculated as 208 km west using the cosine function. The user struggled with applying the Pythagorean theorem correctly due to these errors in component calculation. Proper use of trigonometric functions and careful attention to directional components are essential for accurate displacement results.

PREREQUISITES
  • Understanding of vector addition and displacement
  • Proficiency in trigonometric functions, specifically sine and cosine
  • Familiarity with the Pythagorean theorem
  • Ability to interpret directional components in vector analysis
NEXT STEPS
  • Review trigonometric functions for vector decomposition
  • Practice vector addition problems involving multiple directional components
  • Learn about graphical representation of vectors and displacement
  • Explore advanced topics in physics such as motion in two dimensions
USEFUL FOR

Students studying physics, particularly those focusing on vector analysis and displacement calculations, as well as educators looking for examples of common mistakes in vector addition.

C42711
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I am having a lot of trouble with my homework. If anyone could help me, it would be much appreciated.

The Smith's go on vacation. They travel 16.0 km north/west; then turn 27 degrees to the left and go 135 km; then 294 km south/west. What is their displacement from home?

So I found the X and Y components (using trig functions) of each vector and added them. I then tried to put those numbers into the Pythagorean theorem, but it's not working. I think my X and Y components are wrong. I got the Xs to equal 69 and the Ys to equal 155.3. This is the diagram I made: (the numbers that were given are in red, the rest I found, not sure if they are right though)
[PLAIN]http://img257.imageshack.us/img257/7742/78747381.png
By c42711 at 2011-10-30
 
Last edited by a moderator:
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Yes, something wrong with those x y components. The 294 SW vector has x component 294*cos(45) = 208 west. So your total of 69 is way too small. Got your calculator set on degrees? Note that two of the y components are north while the third one is south.
 

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