Runners Mary & Jane: Relative Velocity Magnitude

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SUMMARY

The discussion focuses on calculating the relative velocity magnitude of two soccer players, Mary and Jane. Mary runs east at 3.42 m/s, while Jane runs at 2.27 m/s at an angle of 33.4° north of east. To find Jane's velocity relative to Mary, the cosine rule is applied to determine the vector difference. The correct approach leads to a relative velocity magnitude of approximately 2.25 m/s, correcting earlier miscalculations.

PREREQUISITES
  • Understanding of vector addition and subtraction
  • Familiarity with trigonometric functions, specifically sine and cosine
  • Knowledge of the cosine rule in triangle geometry
  • Basic principles of relative motion in physics
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  • Study vector addition and subtraction in physics
  • Learn about the cosine rule and its applications in physics
  • Explore trigonometric functions and their use in resolving vectors
  • Practice problems on relative velocity in two-dimensional motion
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Students studying physics, particularly those focusing on mechanics and motion, as well as educators looking for examples of relative velocity problems.

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Homework Statement



Two soccer players, Mary and Jane, begin
running from approximately the same point
at the same time. Mary runs in an easterly
direction at 3.42 m/s, while Jane takes off in
a direction 33.4◦ north of east at 2.27 m/s.
What is the magnitude of the velocity of
Jane relative to Mary?
Answer in units of m/s.

Homework Equations





The Attempt at a Solution


I tried the pythagorean method and trig identities but coming with wrong answers.
Answers i got: 2.25,and 1.25
 
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If O is the starting point, then OA be the velocity vector of Mary and OB be the velocity vector of Jane. The vector AB will be the velocity of Jane with respect to Mary.
Use co-sine rule to find AB.
 

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