Anonymous
Anonymous asked in Science & MathematicsPhysics · 1 decade ago

A car is driven 125 km west and then 80 km southwest. What is the displacement of the car from the point of...?

A car is driven 125 km west and then 80 km southwest. What is the displacement of the car from the point of origin (magnitude and direction)?

kilometers?

degrees south of west ?

2 Answers

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  • 1 decade ago
    Best Answer

    Use the cosine rule. Drawing out the vectors (first draw a line 125km west, then attach a line 80km to the end of it at an angle of (180-45=)135degrees). You can then use the cosine formula a^2=b^2 + c^2 - 2bcCOSA. This will give you the magnitude (the line joining the two lines in the diagram). The direction is simple -22.5 degrees to the horizontal as you have drawn an isoceles triangle.

  • Steve
    Lv 7
    1 decade ago

    D = √[125² + 80² - 2*80*125*cos135°]

    Θ = arcsin[80*sin135°/D]

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