Position vector and magnitude problem

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SUMMARY

The problem involves calculating the y-component of a position vector in the first quadrant, given an x-component of 6.0m and a magnitude of 10m. The relationship between the components and the magnitude can be understood through the Pythagorean theorem, where the magnitude represents the hypotenuse of a right triangle formed by the x and y components. The y-component can be calculated using the formula: y = √(magnitude² - x²), resulting in a y-component of 8.0m.

PREREQUISITES
  • Understanding of vector components and their representation
  • Knowledge of the Pythagorean theorem
  • Familiarity with right triangle properties
  • Basic algebra skills for solving equations
NEXT STEPS
  • Study vector addition and subtraction in physics
  • Learn about vector magnitude calculations
  • Explore applications of the Pythagorean theorem in physics
  • Investigate trigonometric functions related to vector components
USEFUL FOR

Students in physics or mathematics, educators teaching vector analysis, and anyone seeking to understand the relationship between vector components and their magnitudes.

xgoddess210
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Homework Statement



A position vector in the first quadrant has an x-component of 6.0m and a magnitude of 10m

What is the value of its y-component?

Homework Equations



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The Attempt at a Solution



Well I originally thought I could draw a graph where x=6 and y=...then I realized i was solving for y. I don't know what the magnitude bit means. I thought it meant direction, but I don't see how that applies or would help me solve the problem. A little advice on how to solve this problem would be lovely!
 
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Treat this as a right angle triangle

The magnitude would be the hypotenuse in this case
 

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