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Emergency Landing

  1. Aug 31, 2004 #1
    Emergency Landing. A plane leaves the airport in Galisto and flies a distance 155 km at an angle 68.0 Degrees east of north and then changes direction to fly a distance 270 km at an angle 48.0 degrees south of east, after which it makes an immediate emergency landing in a pasture.


    1.) When the airport sends out a rescue crew, how far should this crew fly to go directly to this plane? <--- know how to do this already and got the answer

    2.) In which direction? (Express your answer as an angle measured south of east). <---- need help for this

    ok i need help on #2, here's my work....

    155cos(22)i +155sin(22)j
    270sin(42)i +270cos(42)J

    add those....

    324.37i + 258.7j

    arctan(y/x) = arctan(258.7/329.37) = 38 Degrees <--- my answer... What am i doing incorrectly? (please help within the next 5 hours if you can, that's when the hw is due). thanks
     
  2. jcsd
  3. Aug 31, 2004 #2

    chroot

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    How did you arrive at your second vector (270 sin 42, 270 cos 42)?

    It seems to me it should be (270 cos -48, 270 sin -48).

    - Warren
     
  4. Sep 1, 2004 #3
    155*cos(22) + 155sin(22)
    270*cos(-48) + 270sin(-48)
    -----------------------------
    324.37 + (-142.58)

    arctan (-142.58/324.37) = -24 Degrees south of east (answer must be in south of east)

    is it ok to have a negative answer?
     
  5. Sep 1, 2004 #4

    chroot

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    Angles increase counterclockwise from the positive x-axis. Negative angles increase clockwise. -24 degrees is in the southeast quadrant. It's just 24 degrees south of east. Draw a picture if you don't see it.

    - Warren
     
  6. Sep 1, 2004 #5
    Helpppp

    Hey... I am soo confused. What answer do you get so that I can see what the heck I am doing wrong?
     
  7. Sep 1, 2004 #6

    chroot

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    Sharayah,

    It is our policy not to show explicit answers, but only provide a "path" the student might follow to solve the problem.

    What exactly are you confused about? Have you been assigned the same question?

    - Warren
     
  8. Sep 1, 2004 #7
    Blah

    I need help on the first question.
     
  9. Sep 1, 2004 #8
    How do I approach it?
     
  10. Sep 1, 2004 #9

    chroot

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    Sharayah,

    As we have explained already in this thread, break each vector into components, then add the components. The length of a vector (x1, x2) is

    [tex]L = \sqrt{x_1^2 + x_2^2}[/tex]

    which is nothing more than the Pythagorean theorem.

    - Warren
     
  11. Sep 1, 2004 #10
    That is odd? I tryed that and ended up with the answer 307 km. Is that right? Ohh and sorry I barely came into the thread.
     
  12. Sep 1, 2004 #11

    chroot

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    Sharayah,

    It doesn't seem to be correct. Please show me the steps you used to come up with 307 km.

    - Warren
     
  13. Sep 1, 2004 #12
    I took 155^2 and added 265^2.... then took the sqrt of that

    In numerical terms sqrt(155^2+265^2)
     
  14. Sep 1, 2004 #13

    chroot

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    And where did you come up with the 155 and 265?

    - Warren
     
  15. Sep 1, 2004 #14
    Emergency Landing. A plane leaves the airport in Galisto and flies a distance 155 at an angle 68.0 east of north and then changes direction to fly a distance 265 at an angle 48.0 south of east, after which it makes an immediate emergency landing in a pasture.
     
  16. Sep 1, 2004 #15
    Aren't those my two x distances?
     
  17. Sep 1, 2004 #16

    chroot

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    The problem posted originally had 270 km as the magnitude of the second vector, not 265 km.

    What makes you think you can just add the lengths of the vectors in the way you suggested? As I explained, you need to break the vectors into components and then add the components to find the sum of the vectors. Do you know how to do this?

    - Warren
     
  18. Sep 1, 2004 #17
    I added vectors and got:

    x(crew) = sin68*155+cos48*270
    y(crew = cos68*155-sin48*270

    took arctan(x/y) and got 23.7.. degrees south of east
     
  19. Sep 1, 2004 #18
    I am sorry... I do not know how... I am new in physics and have not had a math class in over 2 years... so I am a little lost... but I should get it.
     
  20. Sep 1, 2004 #19

    chroot

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    Do you know what it means to represent a vector in terms of its components?

    - Warren
     
  21. Sep 1, 2004 #20
    The components are the 'getting the sin and cos' right? If so I need a little guidence on how to determine wether or not it is cos or sin?!
     
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