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Tough Math

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Suppose the ball was 3.24 feet above ground when it was hit, and that it reached a maximum height of approximately 102.51 feet when it had traveled a ground distance of approximately 214.26 feet. The ball lands after traveling a ground distance of approximately 432 feet.

Find an equation of the form y = C(x-z1)(x-z2) where z1 and z2 are the zeros (or roots) of the quadratic polynomial (or x-intercepts of the graph) and C is a scaling constant that needs to be determined.

Thanks!

  • Tough Math -

    I guess we are assuming that the path will be a parabola

    make the following sketch
    on the x-axis, label 3 points A, B , and C
    where A is where the ball is hit,
    B is the maximum point, and
    C is the place where the Ball hits the ground
    sketch the parabola, and continue it to the left of A to hit the origin at O

    so C is (217,74)
    AB = 214.26
    but B must be the midpoint of OC
    so BC = 432-214.26 = 217.74
    then OA = 217.74-214.26 = 3.48 OC = 432+3.48 = 435.48
    so parabola =
    y = C(x-0)(x-435.48)
    but (217.74 , 102.51) lies on it (the vertex)
    102.74 = C(217.74)(-217.74)
    C = -.00216

    y = -.00216x(x-435.48)

    check:
    if x = 3.48 , the height should be 3.24 ft
    y = -.00216(3.48)(-432)
    = 3.247 YEAHHHH!

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