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Math Help - How do I derive this equation?!? HELP!!!

  1. #1
    Newbie
    Joined
    Aug 2008
    Posts
    6

    Question How do I derive this equation?!? HELP!!!

    I started with the equation:
    y=yinitial + (vinitialsintheta)t -1/2gt^2

    I plugged in t=x/(vinitialcostheta)

    to get: y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]

    Using derivatives, how do I get from this equation:

    y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]

    to this equation:

    (dy)/(dtheta)=
    x(sec^2theta)-[(gx^2(tantheta)(sec^2theta))/(vinitial^2)]

    I am completely and totally and utterly confused, bewildered, perplexed, and a list of other things.
    Plese help!!!!!
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  2. #2
    MHF Contributor
    Joined
    Apr 2005
    Posts
    1,631
    You just have to differentiate the
    y=yinitial + x (tantheta) - [(gx^2)/(2(vinitial^2)(cos^2theta))]
    with respect to theta.
    Then you will arrive at the last line.

    Remember that differentiating with respect to theta here means y_initial is constant, and x is constant too.
    Of course the g and the V_initial are constants also.

    Why not write V_initial as Vo, Y_initial as Yo?
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