Runners Mary & Jane: Relative Velocity Magnitude

AI Thread Summary
To determine the magnitude of Jane's velocity relative to Mary, the correct approach involves vector subtraction. Mary runs at 3.42 m/s east, while Jane runs at 2.27 m/s at an angle of 33.4° north of east. The relative velocity can be calculated using the cosine rule to find the resultant vector. Previous attempts using the Pythagorean theorem yielded incorrect results, indicating the need for proper vector analysis. The final answer should be expressed in meters per second (m/s).
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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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