Solving a Vector Problem in the xy Plane

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SUMMARY

The discussion centers on solving a vector problem in the xy plane involving a vector with a magnitude of 80.0 units and a y component of -60.0 units. The two possible x components are calculated using the Pythagorean theorem, yielding values of 60.0 units and -60.0 units. When the x component is constrained to be positive, the resultant vector that, when added to the original vector, results in a vector of 70.0 units in the -x direction is determined to have a magnitude of 10.0 units and a direction of -180 degrees. The relationship between the components x, y, and the magnitude r is defined by the equation r = √(x² + y²).

PREREQUISITES
  • Understanding of vector components in the xy plane
  • Knowledge of the Pythagorean theorem
  • Familiarity with vector addition and resultant vectors
  • Basic trigonometry related to angles and magnitudes
NEXT STEPS
  • Study vector decomposition and addition techniques
  • Learn about the applications of the Pythagorean theorem in physics
  • Explore vector magnitude and direction calculations in detail
  • Investigate the use of unit vectors in representing direction
USEFUL FOR

Students and professionals in physics, engineering, and mathematics who are working with vector analysis and require a solid understanding of vector components and their interactions in the xy plane.

jpodo
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Here is the problem I can't solve:

You are given a vector in the xy plane that has a magnitude of 80.0 units and a y component of -60.0 units.

(a) What are the two possibilities for its x component?

(b) Assuming the x component is known to be positive, specify the vector which, if you add it to the original one would give a resultant vector that is 70.0 units long and points entirely in the -x direction. (looking for Magnitude + Direction)
 
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Suppose that a vector has the components x and y, and a magnitude r. What's the equation that links x, y and r?
 

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