Runners Mary & Jane: Relative Velocity Magnitude

AB^2 = OA^2 + OB^2 - 2(OA)(OB)cos(33.4)= (3.42)^2 + (2.27)^2 - 2(3.42)(2.27)cos(33.4)= 14.71 - 15.48cos(33.4)= 14.71 - 12.96= 1.75Therefore, the magnitude of the velocity of Jane relative to Mary is √1.75 m/s.In summary, to find the magnitude of the velocity of Jane relative to Mary, we use the co-sine rule to find the vector AB, which is the velocity of Jane with respect to
  • #1
yang09
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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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  • #2
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.
 

FAQ: Runners Mary & Jane: Relative Velocity Magnitude

What is relative velocity magnitude?

Relative velocity magnitude is the measurement of the speed and direction of an object or person in relation to another object or person.

How does relative velocity magnitude apply to runners Mary & Jane?

In the case of runners Mary & Jane, relative velocity magnitude refers to the speed and direction at which they are moving in relation to each other.

Why is it important to consider relative velocity magnitude in running?

Relative velocity magnitude is important in running because it can affect the outcome of a race. If one runner has a higher relative velocity magnitude than the other, they will reach the finish line first.

How is relative velocity magnitude calculated?

Relative velocity magnitude is calculated by taking the difference between the velocities of the two runners and considering their direction of motion. This can be done using vector addition or the Pythagorean theorem.

What factors can affect relative velocity magnitude in running?

Factors that can affect relative velocity magnitude in running include the individual speeds and directions of the runners, wind resistance, and terrain. Additionally, any external forces, such as a tailwind or a downhill slope, can also impact relative velocity magnitude.

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