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Find the place of the explosion

  1. Feb 22, 2014 #1
    A missile is fired at speed V0 at an angle 450. The missile exploded into two parts when reaches the maximum height. The part of mass m1 is thrown back at speed V1 relative to the missile speed before the explosion (V1>V0). From the shot till the explosion the wind was blown that exerts a friction force Ffriction =−kV. Exactly at the explosion the wind stops to blow. Find where the explosion accrues.




    Why in finding the y cordinate there is no use of the friction force? the answer says: yexplosion=V0sin45∗texplosion−0.5∗g∗t2explosion while in finding the x coordinate there is a use, didn't friction have to be taken into consideration in both coordinates? Does friction force is only horizontal and not opposite the direction of the velocity?
     
  2. jcsd
  3. Feb 22, 2014 #2

    tiny-tim

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    hi user5! :wink:
    yes, i think you're right, and that equation is wrong :smile:

    the friction seems to be opposite to the velocity,

    so the governing vertical equation should be y'' + ky + g = 0
     
  4. Feb 22, 2014 #3
    thank you very much!
    may you help me with solving this equation?
     
  5. Feb 23, 2014 #4

    tiny-tim

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    hi user5! :smile:

    there's a standard method, which is to write d/dx = D, making it:

    (D2 + kD + g)y = 0​

    you then factor that to (D - a)(D - b)y = 0

    and the solutions are:

    y = C1eax + C2ebx if a ≠ b

    y = (C1 + C2x)eax if a = b :wink:
     
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