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20 January, 08:10

The path of a football kicked by a field goal kicker can be modeled by the equation y = - 0.03x2 + 1.53x, where x is the horizontal distance in yards and y is the corresponding height in yards.

Q1: What is the football's maximum height? Round to the nearest tenth.

Q2: How far is the football kicked?

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Answers (2)
  1. 20 January, 08:25
    0
    You can find the distance kicked by solving for x:-

    -0.03x^2 + 1.53x = 0

    x (-0.03x + 1.53) = 0

    x = 0 (this is the height when he first kicks)

    -0.03x + 1.53 = 0

    x = - 1.53 / - 0.03 = 51 yards

    So Q2 is 51 yards
  2. 20 January, 08:36
    0
    Maximum height occurs when the velocity, derivative of the height function, is equal to zero ...

    dy/dx=-0.06x+1.53, dy/dx=0 when 0.06x=1.53, x=25.5 yds

    The maximum height is then found using this x in the height equation ...

    h (25.5) = 19.5 (to nearest tenth)

    I assume they want to know the maximum distance that the football travels before it hits the ground ... when h=0 that will represent total distance traveled when we solve for x ...

    -0.03x^2+1.53x=0

    1.53=0.03x

    x=51 yds
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