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While exploring a cave, a spelunker starts at the entrance and moves the following distances: 75.0 m north, 225 m east, 160 m at an angle 30.0° north of east, and 150 m south. Find the resultant displacement from the cave entrance.

  • physics -

    You have four vectors.
    For each one resolve them into North and east components.
    Adding the North components.
    N= 75 + 0 + 125 sin(30) - 150 = - 12.5 m
    And adding the east components we get
    E = 0 + 250 + 125 cos(30) + 0 = 358.25

    The magnitude of the result is found by Pythagoras' theory
    C = sqrt (a^2 + b^2)
    = 358 m to three significant figures.

    And the angle is south of east.
    found by arctan (12.5/358.25)
    = 2 degrees south of East.

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