666 asked in Science & MathematicsPhysics · 10 years ago

a lost hiker radios you and tells you...?

...he walked 8.5 km south then turned right 37 degrees and walked 4.2 km. what's his displacement

some physics help?! please i have no idea how to do this!

2 Answers

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  • 10 years ago
    Best Answer

    1. Draw a vector digram, 8.5 km south, then 4.2 km S37W

    2. Use cosine Law c^2 = a^2+b^2-2ab cos c

    c^2 = 8.5^2 + 4.2^2 - 2*8.5*4.2 cos (180-37)

    c^2 = 72.25 + 17.64 + 57

    c^2 = 146.9

    c = 12.1 km

    3. Use sine Law to find angle

    12.1/sin 143 = 4.2/ sin X

    sin X = 0.2

    X = 12

    Final Displacement is 12.1 km 12 degrees West of South

  • Jacy
    Lv 7
    10 years ago

    Draw a vector diagram of each leg of the trip so that you may

    determine the North(+)/South(-) and East(+)/West(-):

    [i.e.,y component and x component, respectively,] of his

    movement.

    For the 8.5 km south leg denote by: -8.5 km S.

    For the 37 deg.right turn and his 4.2 km distance covered,

    use right triangle trigonometry:

    4.2 cos37 north => 4.2*0.7986 = 3.35 km N.

    4.2 sin37 east => 4.2*0.6018 = 2.5 km E

    Now, collect and algebriacally sum respective components:

    y component: => -8.5 + 3.35 = -5.15 km

    x component: => 2.5 km

    Then calculate the total displacement using:

    d = √ x² + y² = √ 2.5² + (-5.15)² = 5.72 km

    Hope this helps!

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