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Homework Help: Resultant displacement and angle

  1. Aug 29, 2006 #1
    While exploring a cave, a spelunker starts at the entrance and moves the following distances. She goes 69.7 m north, 246.8 m east,127.4 m at an angle 37.8 (degrees) north of east, and 127.4 m south. What is the resultant displacement from the cave enterance? The angle should be positive between 0 and 360.

    I drew a diagram not 100% accurate but enough to give me a picture. And the resultant displacement I took to be the distance from point A to point D (start point to end point). The equations I used are as follows:
    ax= 69.7 cos(90) ay= 69.7 sin(90) = 0, 69.7
    bx= 246.8 cos (0) by= 246.8 sin (0) = 246.8, 0
    cx= 127.4 cos(37.8) cy= 127.4 sin(37.8) = 100.7, 78.1
    dx= 127.4 cos(90) dy= 127.4 sin(90) = 0, 127.4

    I found Rx = 347.5
    Ry = 275.2

    R = (347.5^2 + 275.2^2)^1/2
    = 443.2m to be the resultant displacement

    angle = tan= 275.2/347.5= 38.4 degrees

    Is this the right method?
  2. jcsd
  3. Aug 29, 2006 #2

    Doc Al

    User Avatar

    Staff: Mentor

    Rewrite that last equation. If "north" is at an angle of 90 degrees, then south must be directly opposite, which is 270 degrees (or -90 degrees).

    (Other than that error, your method looks just fine.)
    Last edited: Aug 29, 2006
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