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Need help deriving the general maximum height equation

  1. Nov 18, 2012 #1
    1. The problem statement, all variables and given/known data
    You need to derive the general maximum height equation for projectile motion. This equation allows you to calculate the maximum height a projectile reaches or could reach during its motion. Like other such equations we derived in this unit, this one is also very short and simple. In this particular equation max height or YMAX can be defined or expressed in terms of Vm, g, θ, and one trig function. there is both a calculus and non-calculus derivation of this particular formula and both require careful and creative thinking.
    -The calculus method begins with using the trajectory equation.
    -The non-calculus method begins with setting up the charts.

    You may choose either method, but you must clearly show every step in the derivation process. Missing or unclear steps will result in a loss of points. Finally clearly write and circle your resulting formula as: YMAX=

    2. Relevant equations
    Trajectory Equation: y=xtanθ-(gx2/2VL2cos2θ)


    3. The attempt at a solution
    After some research I found that the equation should be: YMAX=(Vm2sin2θ/2g)

    I really don't even know where to start on this. He said that the non-calculus method is much easier. Any help would be greatly appreciated!
     
  2. jcsd
  3. Nov 18, 2012 #2

    mfb

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    2016 Award

    Staff: Mentor

    You can split the movement in horizontal and vertical motion and ignore the horizontal part.

    Energy conservation is one way to get the maximal height, equations for a free fall will work, too.
    In terms of the calculus method: Try to find the derivative of y with respect to x. Which value do you expect at the highest point?
     
  4. Nov 18, 2012 #3
    Ok, so I split it into Vert and Horiz, then ignored the Horiz. I would get:

    Vf = -Vmsin(θ)
    Vi = Vmsin(θ)
    d = y
    t = t
    a = g

    Is that correct for the chart?

    Then I would just have to solve for y and ignore time, using this equation:
    Vf2 = Vi2 + 2ad
    then
    (-VmSin(θ))2=(VmSin(θ))2+2(g)y
    but then I run into the problem where y=0. Which is certainly not what I need.

    What am I doing wrong?
     
  5. Nov 19, 2012 #4

    mfb

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    Staff: Mentor

    I do not understand what you are doing there.

    You could try to calculate the time from launch to highest point, for example.
     
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