Position vector and magnitude problem

AI Thread Summary
To find the y-component of a position vector with an x-component of 6.0m and a magnitude of 10m, one can apply the Pythagorean theorem, treating the components as sides of a right triangle. The magnitude represents the hypotenuse, so using the equation \( \text{magnitude}^2 = x^2 + y^2 \) helps solve for y. Substituting the known values, \( 10^2 = 6^2 + y^2 \), leads to \( y^2 = 100 - 36 \), resulting in \( y^2 = 64 \). Therefore, the y-component is 8.0m. Understanding the relationship between the components and the magnitude is crucial for solving vector problems.
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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



?

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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