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Ricardo and Jane are standing under a tree in the middle of a pasture. An argument ensues, and they walk away in different directions. Ricardo walks 28.0 m in a direction 60.0 ∘ west of north. Jane walks 16.0 m in a direction 30.0 ∘ south of west. They then stop and turn to face each other.(a) What is the distance between them? (b) In what direction should Ricardo walk to go directly toward Jane?

User Jazzybazz
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2 Answers

4 votes

Final answer:

The problem requires using vector addition to find the resultant displacement vector including the distance and direction between Ricardo and Jane. This is solved by decomposing their walks into components, summing these components, and then calculating the magnitude and direction of the resultant vector.

Step-by-step explanation:

The question involves vector addition to determine the distance and direction between two people who have walked in different directions. To solve this, we must break each person's walk into north-south and east-west components, add the components separately, and then use the Pythagorean theorem and trigonometry to find the resultant vector.

For Ricardo, who walks 28.0 m 60.0° west of north, his northward component is 28.0 m * cos(60°) and his westward component is 28.0 m * sin(60°). Jane, who walks 16.0 m 30.0° south of west, has a westward component of 16.0 m * cos(30°) and a southward component of 16.0 m * sin(30°).

Summing up these components, we can then find the distance between them using the Pythagorean theorem and the direction using arctan of the ratio of the north-south to east-west components. Ricardo should walk in the direction of the angle we calculate to go directly toward Jane.

User Dyary
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1 vote

Answer:

Check attachment

Step-by-step explanation:

Ricardo and Jane are standing under a tree in the middle of a pasture. An argument-example-1
User RetiredGeek
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