Vector Components HW: Find Distance/Dir from Lake B to Base Camp

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SUMMARY

The discussion focuses on calculating the distance and direction from Lake B back to Base Camp using vector components. The plane first travels 280 km at 20 degrees north of east to Lake A, then 190 km at 30 degrees west of north to Lake B. The calculations involve using trigonometric functions to determine the x and y components of each leg of the journey. The user initially miscalculated the components and sought clarification on the correct application of the cosine function for the angle at Lake B.

PREREQUISITES
  • Understanding of vector components and trigonometric functions
  • Familiarity with the cosine and sine functions in physics
  • Knowledge of how to calculate distances using the Pythagorean theorem
  • Ability to interpret angles in standard position
NEXT STEPS
  • Review trigonometric identities and their applications in vector calculations
  • Practice drawing vector diagrams to visualize component addition
  • Learn about the Law of Cosines for non-right triangles
  • Explore vector addition in two dimensions using software tools like GeoGebra
USEFUL FOR

Students studying physics or mathematics, particularly those focusing on vector analysis and trigonometry, as well as educators seeking to enhance their teaching methods in these subjects.

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Homework Statement



A plane flies from base camp to lake A, a distance of 280km, at a direction of 20 degrees north of east. After dropping thr supplies, it flies to lake B which is 190km and 30 degrees west of north from lake A. Determine the distance and direction gtom lake B to the base camp

Homework Equations


Axcos theta
Bysin theta

r= Sq rt (X^2 + y^2)

tan - theta = y/x


The Attempt at a Solution



280 cos 20 = 263
280 sin 20 = 95.8

190cos -30 = 184.5
190sin -30 = -95

I tried to add up the components but it doesn't end up being the rigth answer from the book.
 
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Perhaps recalculate those numbers. In particular what is 190*cos(-30)?
 
Did you draw a diagram? What did you get for the x and y components of the final vector?
 

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