Pregunta
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  • Each bounce is modelled by the equation .
  • If the ball continued to bounce, it would eventually converge with the horizontal
    16 metres from point .
    (1) Determine the length of AB.
    IEB Copyright 20222
    NATIONAL SENIOR CERTIFICATE: MATHEMATICs: PAPERI
    (2) What is the maximum height reached by the ball between points B and C?

Ask by Hill Alexander. in South Africa
Nov 02,2024

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The length of AB is 16 meters. The maximum height reached by the ball between points B and C is the y-coordinate of the vertex, which can be found by substituting the x-coordinate of the vertex into the equation .

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Extra Insights

To solve for the length of AB using the provided equation and knowing that it converges horizontally at 16 meters, we recognize that the vertex, represented by , will be the highest point of the bounce. Since it converges at 16 meters, AB’s length is directly related to how high the ball reaches and at what distance it lands.
Assuming B is at its peak, it drops back towards the horizontal line at . Since the maximum height occurs at , and the shape of the parabola approaches zero at both ends, the distance AB will equal the vertex subtracted from the total distance of 16 meters (i.e., wow! It’s quite a numerical feat to calculate without the exact coordinates!).
Moving on to the maximum height between points B and C, we see that the peak of each bounce can be evaluated by substituting the values of p and q into the vertex form of a parabola. So, if you have the coordinates of B, plug them into the equation! The y-value at this vertex will give you the maximum height reached, which is bound to be impressive - keep those calculations squarely in your line of sight while tracking those bounces!

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