The distance from the edge of the centre circle toward the goal and y is the height of the ball.?

A soccer player kicks the ball from a position 17.5 m in front of the goal line. The quadratic function y=-0.05(x-20)(x-40)   describes the path of the ball, where x is the distance from the edge of the centre circle toward the goal and y is the height of the ball.

a. What are the coordinates of the points where the ball theoretically touches the ground?

Update:

b. What is the maximum height of the ball during its flight

1 Answer

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  • Ash
    Lv 7
    1 month ago
    Favorite Answer

    y=-0.05(x-20)(x-40) .....(1)

    When the ball touches the ground, y = 0 

    So we need to find x, when y = 0

    Now plug in (1)

    0=-0.05(x-20)(x-40)

    0 = (x-20)(x-40)

    x = 20 and x = 40

    The ball touches the ball at 40 m from the edge of the centre circle

    b. At max height vertical velocity = 0

    vertical velocity = y'

    y' = -0.05[(x-40) + (x-20)]

    0 =  -0.05(2x-60)

    2x-60 = 0

    2x = 60

    x = 30

    At x=15, find y

    y = -0.05(30-20)(30-40) = 5 m

    Max height of the ball = 5 m

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