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Kinetic energy with ariplanes

  1. Feb 2, 2008 #1
    1. The problem statement, all variables and given/known data
    Which has a higher kinetic energy?
    An airplane traveling at the speed of sound or an airplane with half the weight of plane one and traveling at 2 times the speed of sound?

    2. Relevant equations
    KE = 1/2 mv^2

    3. The attempt at a solution
    I think I am just get mixed up on words. If they were the same weight the plane going twice as fast would have 4 times the kinetic energy. (v=2^2=4).
    I think I am going the wrong direction. Would their kinetic energy be the same? Since plane two weight is half but double the speed. Help
  2. jcsd
  3. Feb 2, 2008 #2
    E1 = (1/2)(m)(v^2)

    E2 =(1/2)(0.5m)(2v^2)
    E2 =(.5)(2^2)(1/2*m*v^2)
    E2 =(.5)(2^2)(E1)
    E2 = 2E1

    I think you multiplied the final 2 by the half that is in the equation for kinetic energy.
  4. Feb 2, 2008 #3
    Since the kinetic energy depends on the speed _squared_, doubling the speed will have more effect than doubling the mass. Try calculating both KE's.
  5. Feb 2, 2008 #4
    I think I have it. Plane two will have the higher KE since KE is quadrupled with increase in speed. The weight is a factor but not as much as speed. Thanks
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