Physics

Question

Find the resultant displacement of a bear searching for berries on the mountain. The bear heads 55.0º north of west for 15.0 m; then it turns and heads to the west for another 7.00 m. (Use trigonometry to answer, but remember to draw a diagram to help your understanding.)

2 Answer

  • North component: y = 15.0 m * sin 55.0º = 12.3 m 
    West component: x = 15.0 m * cos 55.0º + 7.00 m = 15.6 m 

    so his heading, measured from West, is 
    Θ = arctan(y/x) = arctan0.787 = 38.2º N of West 

    and measured from North is 
    φ = arctan(x/y) = arctan(1.27) = 51.8º W of North 

    Hope this helps!
  • Answer:

    Resultant, d = 19.9 meters

    Explanation:

    It is given that,

    The bear heads 55 degrees north of west for 15.0 m; then it turns and heads to the west for another 7.00 m. The attached figure shows the whole scenario.

    The net displacement of bear due north is given by :

    [tex]d_n=15\ sin\theta[/tex]

    [tex]d_n=15\ sin(55) = 12.28\ m[/tex]

    The net displacement of bear due west is given by :

    [tex]d_w=15\ cos\theta+7[/tex]

    [tex]d_w=15\ cos(55)+7=15.60\ m[/tex]

    Let d is the resultant displacement of a bear searching for berries on the mountain. It can be calculated as :

    [tex]d=\sqrt{d_n^2+d_w^2}[/tex]

    [tex]d=\sqrt{12.28^2+15.60^2}[/tex]

    d = 19.85 meters

    or

    d = 19.9 meters

    So, the resultant displacement of a bear is 19.9 meters. Hence, this is the required solution.

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