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Finding an equation of motion

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data

    From a height of 18 meters above ground, an object is thrown vertically upwards at a speed of 30m/s. Find the equation where height h depends on time t. Find the maximum height of the object.

    2. Relevant equations

    h=h0+v0t-(gt^2)/2

    3. The attempt at a solution

    The equation of motion of an object thrown vertically upwards is h=h0+v0t-(gt^2)/2
    By inserting h0=18 and v0=30 we get
    [itex]h=18+30t-(gt^2)/2[/itex], which is the correct answer. When t=3, h is max at 63.
    Now my problem here is that instead of finding the aforementioned equation of motion in a book, i was supposed to create it myself, using differential equation methods. How?
     
    Last edited: Mar 14, 2013
  2. jcsd
  3. Mar 14, 2013 #2

    HallsofIvy

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    Once the ball have been thrown up it has accelration -g, due to gravity. Acceleration is the derivative of velocity and velocity is the derivative of distance (height here).

    So your differential equations problem is [itex]d^2h/dt^2= -g[/itex] with initial values h(0)= 18, h'(0)= v(0)= 30.
     
  4. Mar 14, 2013 #3

    Dick

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    You want to start from using that the derivative of the velocity is equal to the acceleration. So v'(t)=(-g). Integrate both sides to get v(t). Determine the constant of integration. Then v(t)=h'(t), so integrate again to get h(t)
     
  5. Mar 14, 2013 #4
    Thanks for helping me out :)
     
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