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Math Help - prove this:projectiles questions

  1. #1
    Junior Member silvercats's Avatar
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    prove this:projectiles questions

    Object is projected from point O passes through point A and B.vertical distance between O-A is am,horizontal distance is bm.Vertical distance to B is bm and horizontal distance is am.

    show that object's horizontal range is

    (a+ab+b)m/(a+b)

    what I did was:

    O-A
    bm=V cos Θ*t
    t=x/V cos Θ

    O-A
    am=v Sin Θ*t-g/2*t
    am=V sin Θ(bm/V cos Θ)-g/2 *(bm/V cosΘ)
    A-B
    am=V cos Θ*t
    t=x/V cos Θ
    A-B
    bm=v Sin Θ*t-g/2*t
    bm=V sin Θ(am/V cos Θ)-g/2 *(am/V cosΘ)
    got two equations.but now what??
    Thank you for your time
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  2. #2
    MHF Contributor
    skeeter's Avatar
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    Quote Originally Posted by silvercats View Post
    Object is projected from point O passes through point A and B.vertical distance between O-A is am,horizontal distance is bm.Vertical distance to B is bm and horizontal distance is am.

    show that object's horizontal range is

    (a+ab+b)m/(a+b)

    what I did was:

    O-A
    bm=V cos Θ*t
    t=x/V cos Θ

    O-A
    am=v Sin Θ*t-g/2*t
    am=V sin Θ(bm/V cos Θ)-g/2 *(bm/V cosΘ)
    A-B
    am=V cos Θ*t
    t=x/V cos Θ
    A-B
    bm=v Sin Θ*t-g/2*t
    bm=V sin Θ(am/V cos Θ)-g/2 *(am/V cosΘ)
    got two equations.but now what??
    Thank you for your time
    consider the parabolic trajectory of the projectile in the x-y plane ... it passes thru the points (0,0) , (b,a) , and (a,b)

    mathematically, an inverted parabola that passes thru the origin can be written in the form

    y = kx(R-x)

    where k is a constant and R is the 2nd x-intercept (the "Range" in this case)

    for point (b,a) ...

    a = kb(R-b)

    for point (a,b) ...

    b = ka(R-a)

    now use the two equations to solve for R in terms of a and b.
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  3. #3
    Junior Member silvercats's Avatar
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    ah I didn't think we have to use that kind of equations for this.
    can't we do this using only kinematics equations?
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  4. #4
    MHF Contributor
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    Quote Originally Posted by silvercats View Post
    ah I didn't think we have to use that kind of equations for this.
    can't we do this using only kinematics equations?
    you can, but you'll end up having to eliminate the parameter of time anyway to arrive at the range in terms of a and b ... you end up with essentially the same equation I derived, just a bit messier w/ the constants.
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