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Rocket Launch Kinematics motion

  1. Dec 13, 2013 #1
    1. The problem statement, all variables and given/known data

    You're at a mission control for a rocket launch, deiciding whether to let the launch proceed. A band of clouds 5.3km thick extends upwards from 1.9km altitude. The rocket will accelerate at 4.6ms^-2 and it isn't allowed to be out of sight for more than 30s.
    Should the launch be allowed?

    2. Relevant equations

    None.

    3. The attempt at a solution

    Clear skies ranges from y = [0m,1900m]
    Thick cloud ranges from y = [1900m,7200m]

    vf^2 - vi^2 = 2a(yf - yi)
    vf^2 = 2(4.6ms^-2)(1900_
    vf = 132.2ms^-1

    At the instantaneous moment rocket is at position y = 1900m, vf = 132.2ms^-1

    From y = 1900m, vf = 132.2ms^-1 = vi

    yf - yi = vit + 0.5at^2
    yf - yi = 132.2ms^-1 (30s) + 0.5(4.6ms^-2)(30)^2
    yf - yi = 6036m

    [yf - yi] = 6036m > 5300m from t = [0s,30s]

    Launch should be allowed.
     
  2. jcsd
  3. Dec 13, 2013 #2

    haruspex

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    Looks right.
     
  4. Dec 13, 2013 #3
    How would the equation change if the acceleration of the rocket and gravity were included within the parameter? I'm curious.
     
  5. Dec 13, 2013 #4

    Curious3141

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    It already is. The net acceleration after taking into account the opposing deceleration from gravity is 4.6m/s^2. Without gravity, the rocket could presumably accelerate at (4.6 + 9.8) = 14.4 m/s^2. The rocket thrust force is 14.4*M, where M is the mass of the rocket.
     
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