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Math Help - urgent help needed!

  1. #1
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    urgent help needed!

    ok so ive been up all night at this but I dont no what to do!
    so here goes:
    A projectile released with a velocity U m/s at an angle xto the horizontal, just clears two obstacles, both of height h m, whose distances from the point of projection are b m and 3b m respectively. Find the range of the projectile.
    any help or answers would be greatly appreciated. Thanks.
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  2. #2
    MHF Contributor alexmahone's Avatar
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    Quote Originally Posted by totster View Post
    ok so ive been up all night at this but I dont no what to do!
    so here goes:
    A projectile released with a velocity U m/s at an angle xto the horizontal, just clears two obstacles, both of height h m, whose distances from the point of projection are b m and 3b m respectively. Find the range of the projectile.
    any help or answers would be greatly appreciated. Thanks.
    Let the angle to the horizontal be \theta.

    y=xtan\theta -\frac{gx^2}{2u^2cos^2\theta}

    Since the projectile passes through the points (h, b) and (h, 3b), we get

    b=htan\theta -\frac{gh^2}{2u^2cos^2\theta}

    3b=htan\theta-\frac{gh^2}{2u^2cos^2\theta}

    Solve for u and \theta from these equations and substitute in

    R=\frac{u^2sin2\theta}{g}
    Last edited by alexmahone; December 16th 2009 at 05:33 PM.
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  3. #3
    Grand Panjandrum
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    Quote Originally Posted by totster View Post
    ok so ive been up all night at this but I dont no what to do!
    so here goes:
    A projectile released with a velocity U m/s at an angle xto the horizontal, just clears two obstacles, both of height h m, whose distances from the point of projection are b m and 3b m respectively. Find the range of the projectile.
    any help or answers would be greatly appreciated. Thanks.
    Integrate the equations of motion to get the horizontal and vertical displacements as functions of time.

    From the horizontal displacement equation find t in terms of horizontal displacement and substitute this into the vertical equation.

    This gives you a quadratic for the vertical displacement in terms of the horizontal displacement.

    Now use this to complete the solution.

    CB
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  4. #4
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    The flight path will be symetrical about a vertical line at some distance x. But we know that the projectile is at the same height when it is at b and at 3b. Therefore the line of symetry must be located half way between b and 3b, that is at 2b.

    Now you know the projectile is at height 0 m at x=0 and it has a line of symetry at x=2b. So the projectile will again be at height =0 when x = ????
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