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Projectile motion with a region of 0 acceleration

  1. Apr 9, 2009 #1
    1. The problem statement, all variables and given/known data
    I dont know if the title is misleading or not because I cant think of anything better ..

    I need help with something Ive been working on... its not homework...its more of a side project/hobby of mine, but i couldnt figure out where to put this question..

    Basically I need to figure out the x-component of the initial velocity
    So lets call it Vi

    Heres the scenario

    http://img27.imageshack.us/img27/5536/sce1d.jpg [Broken]

    The known values are
    d1= 10
    d2= 10
    d3= 10
    a = 10 during d1 and d3 and a = 0 during d2 (see pic above)
    and t1+ t2 + t3 = 3 seconds


    2. Relevant equations

    Vf = Vi + a*t
    d= Vit + 0.5*a*t^2
    d = v*t (if acceleration = 0)
    vf^2 = vi^2 + 2ad

    So basically I started off with the following 3 equations, I only used the first three equations from above

    d1 = Vi*t1 + 0.5*a*t1^2

    d2 = V2*t2 (since acceleration = 0)
    Since V2 = Vi + at1, then
    d2 = (Vi + a*t1)t2 = Vi*t2 + a*t1*t2

    d3 = V2*t3 + 0.5*a*t3^2
    or in terms of Vi
    d3 = Vi*t3+ a*t1*t3 + 0.5*a*t3^2


    3. The attempt at a solution

    d1+d2+d3= Vi*t1 + 0.5*a*t1^2 + Vi*t2 + a*t1*t2 + Vi*t3+ a*t1*t3 + 0.5*a*t3^2

    Then I rearranged the equation to get

    dtotal = Vi(t1+t2+t3) + (0.5*a*t1^2 + a*t1*t2 + at*t1*t3 + 0.5*a*t3^2)

    Mutiply both sides by 2 to get rid of 0.5

    2*dtotal = 2*Vi(t1+t2+t3) + a(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2)

    After plugging in the known values, this is the point Im stuck at

    60 = 6*Vi + 10(t1^2 + 2*t1*t2 + 2*t1*t3 +t3^2)

    Is there any way I can reduce the above equation knowing t1+t2+t3 = 3 to find out Vi?

    Or maybe Im doing this completely wrong and theres a better way to find out Vi given the scenario??
     
    Last edited by a moderator: May 4, 2017
  2. jcsd
  3. Apr 9, 2009 #2

    rl.bhat

    User Avatar
    Homework Helper

    I can visualize the problem this way.
    A particle is projected with an initial velocity V making an angle of projection theta.When it reaches the maximum height, its velocity is horizontal. It lands on a table of length 10 m with frictionless surface. At the end of the table it travels in the similar way as in the first case with reversed direction.
    With these hints try to solve the problem.
     
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