Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 month ago

a ball is thrown from a balcony that is 20meters above ground. The path of the ball is described by the equation h=a(x-5)^2+22.5.?

Update:

I would like to know the answer to a and c only. I am not sure how to get that answer

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3 Answers

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  • Jeremy
    Lv 6
    1 month ago
    Favorite Answer

    a) The ball falls off from the balcony, which is 20 m high. At the very beginning, there's no horizontal displacement, so: x = 0; h = 20. Therefore:

    20 = a * (0 - 5)^2 + 22.5 ===> 20 = a * 25 + 22.5 ===> 20 - 22.5 = 25a ===>

    ===> -2.5 = 25a ===> a = -2.5/25 = -0.1   

    c) The equation that describes the path is: h = -0.1 * (x - 5)^2 + 22.5.

    x = 5 is the abscissa of the vertex; y = 22.5 is the ordinate of the vertex. 

    (*) The maximum height reached by the ball is given by the ordinate of the vertex of the parabola that describes the path. Hence: h_max = 22.5 m.

    (**) The horizontal displacement of the ball (when it reaches the maximum height) is given by the abscissa of the parabola that describes the path. Hence: x = 5 m.  

  • 1 month ago

    a) At the start h = 20 and x = 0

    so, 20 = a(0 - 5)² + 22.5

    => 20 = 25a + 22.5

    i.e. 25a = -2.5

    Hence, a = -2.5/25 => -0.1

    c) The function is in vertex form, so maximum value occurs when the quadratic term is zero

    Hence, when x = 5 metres

    Then, h = -0.1(5 - 5)² + 22.5

    i.e. h = 22.5 metres  

    A sketch is below.

    :)>

    Attachment image
  • Anonymous
    1 month ago

    Is there any reason you don't pick Best Answers?

    https://au.answers.yahoo.com/question/index?qid=20...

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