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Propagation of error help

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    I slide a ball off of a ramp (the ramp is on a table) and the ball hits the ground and bounces horizontally and vertical.
    I know that horizontal velocity = horizontal distance*sqrt(gravity/2*height) or d*sqrt(g/2h)
    I want to know the equation for calculation error.

    The expression for the error in the horizontal component of ball's velocity is:
    Select one:
    a. error v = v[(error d)/d + (error g)/g +(error h)/h]
    b. error v/2 = v[(error d)/d + (error g)/g +(error h)/h]
    c. error v/4 = v[(error d)/d + (error g)/g +(error 2h)/h]
    d. error v = v[(error d)/d + (error g)/g +(error 2h)/h]
    e. error v/2 = v[(error 2d)/d + (error g)/g +(error h)/h]


    2. Relevant equations



    3. The attempt at a solution
    I think its a. The problem I have is the 2h. I don't know how to deal with it. If v=sqrt(g/h) then I know for sure the answer is a. but since that 2 is there I don't know if the answer is still a.
     
  2. jcsd
  3. Mar 14, 2013 #2

    tms

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    If [itex]x[/itex] is a function of measured variables [itex]u, v, \ldots[/itex],
    [tex]x = f(u, v, \ldots),[/tex]
    then,
    [tex]\sigma_x^2 \approx \sigma_u^2 \left ( \frac{\partial x}{\partial u}
    \right )^2 + \sigma_v^2 \left ( \frac{\partial x}{\partial v} \right )^2
    + \ldots \;.[/tex]
    You should be able to figure it out from there. Except that I think you may have written down the possible solutions incorrectly; aren't there some missing square roots?
     
  4. Mar 15, 2013 #3

    haruspex

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    None of the choices seem right to me.
    Don't worry about the 2 in the 2h. That's just a factor of root 2 on the whole expression. It has no relationship to the h specifically. What matters is the powers of the variables. If e.g. z = A xmyn then Δz/z = m Δx/x + n Δy/y. It's just the normal product rule of differentiation.
     
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