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Coriolis Effect - Vertical Shot, solution through integration?

  1. Dec 28, 2011 #1
    Hi, it's my first time on these forum, so I hope that I made this post correctly.

    I have an example solution to this problem using tensors and matrices ^^ but I wanted to solve the problem in a different way and would like some feedback on whether or not this solution is correct.

    1. The problem statement, all variables and given/known data

    A gun shoots a projectile vertically into the air with an exit velocity of vvert=60ms-1 (assuming the nozzle is at sea level). Calculate the distance Δs, between the starting point and landing point of the projectile. Do this for the latitudes 0° and 51°. (neglect cascading effects)


    2. The attempt at a solution

    Getting the time t for the whole process is a no-brainer:

    v(t) = 0 = vvert-gt , g = const. => t1 = 6.1s => ttotal = 12.2s

    Now to calculate Δs:

    We assume that the earth is an ideal globe, with a radius r = 6370000km. Basic geometry tells us that the distance from the axis of rotation is
    R = sqrt(h(2r-h)) => R = sqrt(r²-r²sin²(α)) , α...latitude => R = r*cos(α)

    The circumference of r(t) is the gives us the orbital velocity vB = const.:

    r(t) = r + ∫v(t)dt

    2∏r(0)/d = vB , d...day

    vB is constant => ω can not be constant:

    ω(t) = vB1/vB21 = u1/u21 = r/r(t)*ω1 (R1/R2 = r1/r2)

    Angular acceleration: w'(t) = - (r*v(t))/(r+∫v(t)dt)² * ω1

    Δω = ω1 ∫ -(r*v(t))/(r+∫v(t)dt)² dt

    Δs = Δω*R*t = r*cos(α)*t*ω1 ∫ -(r*v(t))/(r+∫v(t)dt)² dt

    Thank you for your troubles.
     
  2. jcsd
  3. Dec 28, 2011 #2
    150 views, no replies... did I put this in the wrong section? ;)
     
  4. Dec 30, 2011 #3
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