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Simple Relative Motion Problem

  1. Jan 15, 2013 #1
    1. The problem statement, all variables and given/known data
    A ladybug with a velocity of 10.0mm/s [W] crawls on a chair that is being pulled [50deg N of W] at 40.0mm/s. What is the velocity of the ladybug, relative to the ground?


    2. Relevant equations

    pythag theorum
    component vectors
    sohcahtoa

    3. The attempt at a solution

    Let [N] and [W] be positive.

    Velocity of the ladybug relative to the chair = VLC = 10mm/s [W]
    Components:
    VLCx = 10mm/s
    VLCy = 0mm/s

    Velocity of the chair, relative to the ground = VCG = 40mm/s [W50degN]
    Components:
    VCGx = 40mm/s (cos50) = 25.71150439mm/s
    VCGy = 40mm/s (sin50) = 30.64177772mm/s

    Velocity of the ladybug, relative to the ground = VLG = ?
    Components:
    VLGx = VLCx + VCGx = 35.71150439mm/s
    VLGy = VLCy + VCGy = 30.64177772mm/s

    Direction of VLG
    ∅ (theta?) = tan-1(opposite/adjacent)
    = tan-1(VLGy / VLGx)
    = tan-1(30.64177772mm/s / 35.71150439mm/s)
    = 40.63 degrees

    ∴ VLG = √2214.230088 = 47.05560634mm/s [ W 40.63deg N ]


    I feel that my calculations are correct.
    However, looking up this question on the net shows that people have come to a different end result:
    https://www.physicsforums.com/showthread.php?t=596229

    Specifically, the direction of the resultant vector is different.



    I just want to be sure that my answer is correct before I submit it for marking.
    Thanks.
     
    Last edited: Jan 15, 2013
  2. jcsd
  3. Jan 15, 2013 #2

    gneill

    User Avatar

    Staff: Mentor

    The result of your calculations look okay. You might want to do something about significant figures for the final value before handing it in.
     
  4. Jan 15, 2013 #3
    I haven't really done much math this year. From what I recall, you use the given values in determining the amount of significant digits... you choose the number that has the least amount of sig. digits.

    Both 40.0mm/s and 10.0mm/s have three sig digits.

    So...
    The final, rounded answer should be:

    VLG = = 47.1mm/s [ W 40.6deg N ]

    Correct?
     
  5. Jan 15, 2013 #4

    gneill

    User Avatar

    Staff: Mentor

    Looks good.
     
  6. Jan 15, 2013 #5
    Thanks bros (and broettes).
     
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