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2 dimen kinematics problem

  1. Mar 6, 2007 #1
    1. The problem statement, all variables and given/known data
    [​IMG]

    Xy=2400 m

    2. Relevant equations

    Xy=Voyt + 1/2at^2
    Xx=1/2(Vox+Vx)t

    3. The attempt at a solution

    I calculated the vertical and horizontal velocity components of the given resultant velocity of 240 m/s.

    Voy = 120 m/s
    Vox = 208 m/s

    then i used the vertical component, the given vertical distance and gravity to calculate the time needed for the package to fall to the ground.

    t = 38 s

    then i plugged this into Xx=1/2(Vox+Vx)t to find the horizontal distance the package travelled.

    Xx= 3904

    then i plugged this in with the given vertical distance into tan -1 (y/x) to get an angle of 31 degrees. but the book says 42 degrees! where did i go wrong guys?
     
  2. jcsd
  3. Mar 6, 2007 #2
    you want the arc tan of the final velocities Vyf/Vxf
     
  4. Mar 6, 2007 #3
    hmm why do i want the arc tan of the final velocities and not the arc tan of the distances?

    also, arent the final velocites both = 0 since the package hits the ground
     
    Last edited: Mar 6, 2007
  5. Mar 6, 2007 #4
    denverdoc, I think deserthobo is right is the arctan of distances, the 2.4 km and the horizontal range of the flare.
     
  6. Mar 6, 2007 #5
    hmm...the time needed for the object to fall


    well, vf = vo + at

    vf = 0


    so...
     
    Last edited: Mar 6, 2007
  7. Mar 6, 2007 #6
    ok using vf=vo + at i got 12 s

    i plugged 12 s into x = 1/2(vf + vo)t and then found the arc tan with that number and came up with 62 degrees. doesnt work out.
     
    Last edited: Mar 6, 2007
  8. Mar 6, 2007 #7
    ok guys, if i plug in the horizontal velocity component which is 208 for

    vf and vo

    for

    x=1/2(vf+vo)t

    i will get 2704 m, which when plugged into arc tan (y/x) will give me the angle of 41..5 which when rounded up is 42 degrees. but does it make sense to plug in 208 for both vf and vo?
     
  9. Mar 6, 2007 #8
    ok, t is not just 12, there are some extra digits as well (i'm horrible with sig digs as well :-p)

    also, the horizontal velocity is constant

    and velocity = distance/time

    so, distance = velocity * time

    you know the time, and you know the velocity
     
    Last edited: Mar 6, 2007
  10. Mar 6, 2007 #9
    ok so i did everything following what mybsaccownt said and in the end i came up with 43 degrees. the book says 42 so this method is incorrect!
     
  11. Mar 6, 2007 #10
    I think you and the book are likely bothright, round off error. And i was all wet, in a hurry between patients , and shouldn't have posted.
     
  12. Mar 7, 2007 #11
    Are you a doctor? :)
     
  13. Mar 7, 2007 #12
    guilty as charged, tho a psychiatrist in the minds of many of his fellow physicians has lost any valid claim to the title
     
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