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(Projectile Motion)How to derive the equation?

  1. Apr 17, 2005 #1
    (Projectile Motion)How to derive the equation??

    I made a device which use elastic band to launch a ping pong ball.
    I have measured the distance travelled with different length of stretch at constant 36 degree launch angle. The graph plotted out is kind of curved, not straight line. And now I am asked to derive an equation to determine distance as a function of stretch....
    Does anyone know how to do this? Cuz I spent almost a day still duno how to do it.
  2. jcsd
  3. Apr 17, 2005 #2
    First, determine what kind of relationship it is (i.e. exponential, root...). WHat kind is it?
  4. Apr 17, 2005 #3
    Well... i dont really know actually. I guess its root maybe?
    heres the data
    Stretch(cm) Distance(m)
    10.7 5.684
    15.35 7.955
    20.12 9.98
    24.96 10.365
    29.83 11.725
    Last edited: Apr 17, 2005
  5. Apr 17, 2005 #4
    Wait a minute, let me enter the data in my calc
  6. Apr 17, 2005 #5
    Well, it's hard to tell for sure. If you had more points, it would be easier to determine. The first 3 points look linear, but with the last 2 points, it looks more like a root relationship.
  7. Apr 17, 2005 #6
    oh.... yaa that's what the graph looks like...
    alright maybe I gotta do more points then.
    Anywayz, Thanks a lot!
  8. Apr 17, 2005 #7


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    Homework Helper

    If you think the data is related by a power function you can try a power regression on your calculator. In the old days, the power was usually found by graphing the log of the distance and the log of the stretch to decipher the exponent from the slope of what would then be a linear graph. If your calculator can't do it, I can elaborate on the log-log approach
    Last edited: Apr 17, 2005
  9. Apr 18, 2005 #8
    You may want to try.. y/x and y/x^2 ... y/sqrt(x) and so on, which gets you the constant of proportionality k ... and see which one is more consistent
  10. Apr 19, 2005 #9
    of course it's a curve
    here's the equation

    v=u+at (vertical motion)
    -u sin36=u sin36 -gt
    t=2u sin36/g

    s= u sin36 * 2 u sin36/g
    s= u*u *2 *sin36 *cos36 / g

    mv*v/2= kx*x/2



    s=kx*x *2 *sin36 *cos36 / gm

    as all the other variables remain constant

    if a=k*2 *sin36 *cos36 / gm

    s= a * x^2
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