A soccer player kicks a ball?

A soccer player kicks a ball from the ground to a maximum height of 12 m. The high point in the trajectory of the ball occurs at a distance of 18 m from the kicker. On the downward path, another player heads the ball at a height of 2.2 m from the ground.

a. Write a quadratic function that models the situation.

b. How far from the kicker in the line of the trajectory must a player be to head the

   ball as described? Give the answer to two decimal places.

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1 Answer

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  • david
    Lv 7
    1 month ago

    x = distance from kicker

    y = height of ball

      (0,0)  <<<  original place where ball is kicked

      (18, 12)  <<<  hghest point

      because of symmetry  (36,0) should be another point .. except for the header

      y = ax^2 + bx + c

      0 = a(0) + b(0) + c  ..  c = 0

      

      12 = a(18^2) + b(18)

       0 = a(36^2) + b(36)  ...  b= -36a

      12 = 324a + 18b

       12 = 324a + 18(-36a)  ...  a = -12/324 = -1/27

       b = +4/3

      . . . y = -(1/27)x^2  + (4/3)x  <<<  quadratic

      y = 2.2 .. x = ? . . 

       2.2 = -(1/27)x^2 + (4/3)x  <<<  solve for x

      x = 34.2665 m

      y = -(1/27)x^2 + (4/3)x   for   0 < x < 34.2665

        

       the quadratic must have a limited domain  because of the header

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