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A person walks the path shown below. The total trip consists of four straight-line paths.
Path 1 is 80.0 m due east.
Path 2 is 250.0 m due south.
Path 3 is 130.0 m 30.0° south of west.
Path 4 is 190.0 m 60.0° north of west.
At the end of the walk, what is the person's resultant displacement?

  • physics - ,

    Start the person at (0,0), and calculate the new position after each path.

    After path 1: (80,0)
    After path 2: (80, -250)
    After path 3: x displacement is -130*cos30; y displacement is -130*sin30

    (80 - 130*cos30, -250 -130*sin30)

    After path 4: x displacement is -190*cos30, y displacement is 190*sin30;

    New position is:

    (80 - 130*cos30 - 190*cos30, -250 -130*sin30 + 190*sin30)

    The magnitude of the displacement is (x^2 + y^2)^0.5, where (x,y) is the final position

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