Vectors, Direction, and Net displacement

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SUMMARY

The discussion focuses on solving vector problems involving displacement and direction. The first problem involves a helicopter traveling northwest 70.7 miles, east 100 miles, and south 100 miles, requiring the calculation of its net displacement from the origin. The second problem involves a ship sailing 100 miles northwest and then 141.4 miles south, also necessitating the determination of its final position. The calculations presented utilize trigonometric functions to resolve the vectors into components, confirming that the approach is correct for determining magnitude and direction.

PREREQUISITES
  • Understanding of vector addition and resolution
  • Familiarity with trigonometric functions (sine and cosine)
  • Knowledge of Cartesian coordinate system
  • Basic skills in calculating magnitude and direction of vectors
NEXT STEPS
  • Study vector addition techniques in physics
  • Learn how to resolve vectors into components using trigonometry
  • Explore applications of vectors in navigation and physics
  • Practice solving displacement problems with varying angles and distances
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Students in physics or mathematics, educators teaching vector concepts, and anyone interested in navigation and displacement calculations.

rorushing4283
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I have been working on the following two problems and I can't seem to get any progress.
Any help from anyone would be greatly appreciated. I know it seems simple to those who are familiar but I have no background in this type of equations.

1. A helicopter travels northwest 70.7 miles, then straight east 100 miles, and finally straight south 100 miles. How far and in what direction is it from point of origin?



2. A ship sails 100 miles northwest then 141.4 miles due south. How far and in what direction is it from its starting location?
 
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100 miles NW
141.4 miles S

x=100cos135=-70.71
y=100sin135=70.71

Mag=sqrt(-70.71)^2+(70.71)^2
Mag=sqrt10000
Mag=100miles

is this on the right track for this problem?
 

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