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Equation Rearrangement problem(I think)

  1. May 14, 2017 #1
    1. The problem statement, all variables and given/known data
    The escape velocity for tomahawk missile is which escape the gravitational attraction of the earth is expressed by

    r= radius of earth , g = acceleration due to gravity k,x,y=dimensionless constants
    Determine values for x and y
    2. Relevant equations
    I know velocity is displacement/time , and acceleration is velocity/time, however I have no idea how this relates to the question. Since there are no exact values given, I'm pretty sure I have to isolate x and y.

    3. The attempt at a solution


    kg^xr^y/kr^y = v/kr^y


    This is where I got stuck.Based on the equation above, then kr^y is the value for Time. I have no idea how I'm supposed to isolate the x and y. And I'm not even sure I'm approaching this question correctly
  2. jcsd
  3. May 14, 2017 #2


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    Use dimensional analysis. What are the dimensions of acceleration multiplied by distance?
  4. May 14, 2017 #3


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    You need to find values of x and y so that the left-hand side and the right-hand side of v = kgxry have the same dimensions.

    For example, suppose you were to let x = 1 and y = 1. What would be the dimensions of the right-hand side?
  5. May 14, 2017 #4
    Wouldn't that break the rules of the question?
    The question never did say x and y are equal.
  6. May 14, 2017 #5
    are you sure that g in that equation is g the acceleration . not G the gravitational constant
    i think its G
    becouse the escape velocity Ve=(2GM/r)0.5
    and you can rearange that to get :

    i guess its not that simple
  7. May 14, 2017 #6


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    True. But it never said they couldn't be equal either. :oldsmile:
    Anyway, in solving the problem you will determine whether or not they happen to be equal.
  8. May 14, 2017 #7


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    Hello, patric44. It appears from the statement of the problem that g represents the acceleration due to gravity (apparently at the surface of the earth).

    When helping someone with a question, please don't provide a complete solution. This is against the rules of the forum. Try to provide just enough assistance to get the questioner on track. Thanks.
  9. May 14, 2017 #8
    i dont think that a truly complete solution i mean its only one equation.
    i only wanted to show him if it was G it will be much simpler ... sorry any way :)
  10. May 14, 2017 #9


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