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Math Help - Parametric Application

  1. #1
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    Parametric Application

    If a projectile is fired with an initial velocity of v0 meters per second at an angle α above the horizontal and air resistance is assumed to be negligible, then its position after t seconds is given by the parametric equations

    x = (v_{0}\cos\theta)t

    y = (v_{0}(\sin\theta)t =- \dfrac{1}{2}gt^{2}

    where g is the acceleration due to gravity (9.8 m/s2). (Round your answers to the nearest whole number.) (a) If a gun is fired with α = 30 and v0 = 900 m/s.

    x = (900 m/s\cos30^{o})t

    y = (900 m/s\sin30^{o})t =- \dfrac{1}{2}(9.8 m/s)t^{2}

    x = (900 m/s\dfrac{\sqrt{3}}{2})t

    y = (900 m/s\dfrac{1}{2})t - \dfrac{1}{2}(9.8 m/s)t^{2}

    When will the bullet hit the ground?

    (900 \dfrac{1}{2})t - \dfrac{1}{2}(9.8)t^{2} = 0

    300t - 4.9t^{2} = 0

    t(300 - 4.9t) = 0

    t = 0s

    t = 61.2s

    How far from the gun will it hit the ground?




    t = \dfrac{300}{4.9} = 61


    What is the maximum height reached by the bullet?


    (b) Find the equation of the parabolic path by eliminating the parameter.
    Last edited by Jason76; July 25th 2014 at 08:49 PM.
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  2. #2
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    Re: Parametric Application

    No idea what is going on here.
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