How Do You Solve the Relative Motion Problem Between Mary and Jane?

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To solve the relative motion problem between Mary and Jane, it's essential to break down their movements into components using trigonometry. Mary runs east at 4.45 m/s, while Jane runs at 5.12 m/s at an angle of 63.6 degrees north of east. To find the distance between them after a certain time, use the formula d = rt for each player and apply the Law of Cosines to calculate the resultant distance. The challenge lies in correctly setting up the equations and understanding that the angles involved allow for the use of the Law of Sines or Cosines, even if they aren't right triangles. Properly applying these principles will yield the required distances at both the specified time and when they are 24.3 meters apart.
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1. Two soccer players, Mary and Jane, begin running from nearly the same point at the same time. Mary runs in an easterly direction at 4.45 m/s, while Jane takes off in a direction 63.6o north of east at 5.12 m/s

How long is it before they are 24.3 m apart?

How far apart are they after 4.09 s?

I've tried setting up this equation so many times, but I'm getting no where. I know I cannot use the Pythagorean Theorem so what do I need to do?
 
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Think of the sides as velocity*time ratios. Then use trigonometry to find the third side's ratio. Use d=rt to find your answers.
 
Law of Sines or Cosines perhaps?
 
I thought you could only use those rules in a right triangle where the other two sides were 45 degrees. one of the sides of this right triangle is 63.6 degrees.

I know the problem should be easy, but it keeps fooling me
 

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