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Finding relationship between Range and Launch height

  1. Feb 8, 2017 #1
    1. The problem statement, all variables and given/known data
    I am currently trying to find a way to determine the relationship between launch height and range for a projectile launched at less than horizontal.

    Would vary launch height to and measure range.

    I need a directly proportional equation or at least a linear relationship.

    2. Relevant equations

    In next part

    3. The attempt at a solution

    Sh = Vh*t
    Sv = Vov*t + 1/2*a*t^2

    Where the launch velocity components are:

    Vv = v*sin(launch angle)
    Vh = v*cos(Launch Angle)


    Sh = v * cos(launch angle) * t so t = Sh/v*cos(launch angle)
    Sv = v*sin(launch angle) * t + 1/2*a*t^2

    Substituting time,
    Sv = v*sin(launch angle) * (Sh/ v * cos(launch angle)) + 1/2 * a * (Sh/ v * cos(launch angle))^2

    This is as far as I have got however I need to find a way to show the direct relationship between launch height and range. I am assuming now this isn't possible due to the quadratic, however can anyone think of a solution?
  2. jcsd
  3. Feb 8, 2017 #2


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    Can you solve for the zeros of a quadratic equation (in general)?
  4. Feb 8, 2017 #3
    Yes but having it in a quadratic form won't give a linear relationship. Is there an alternative to my method that would yield a linear relationship between range and launch height?
  5. Feb 8, 2017 #4


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    Gold Member

    Why would you expect to have the relationship be linear? I'm not saying that I KNOW it to be non-linear, but I would have started out with the assumption that it would NOT be, not that it would be.
  6. Feb 8, 2017 #5
    For the purpose of the school report, we must have a linear relationship in the form y = mx +c, so that the m value can be compared to measured values to prove the accuracy of the data.
  7. Feb 8, 2017 #6


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    Gold Member

    Well, maybe the relationship IS linear, I just would not have expected it to be.
  8. Feb 9, 2017 #7


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    Science Advisor

    Why must the relationship be linear to compare measured to predicted values? You could have some other functional form and still compare, couldn't you?
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