The building should be 1.024 meters high and unfortunately there are no buildings with such height in the world.
In this question we must use definition of geometric progression to predict initial height ([tex]h_{o}[/tex]), in meters, in terms of current height ([tex]h[/tex]), in meters, and number of bounces experimented by the ball ([tex]n[/tex]). The expression is described below:
[tex]h = h_{o}\cdot \left(\frac{1}{2} \right)^{n}[/tex] (1)
If we know that [tex]n = 10[/tex] and [tex]h = 1\,m[/tex], then the initial height is:
[tex]1 = h_{o}\cdot \left(\frac{1}{2} \right)^{10}[/tex]
[tex]h_{o} = 2^{10}[/tex]
[tex]h_{o} = 1024\,m[/tex]
The building should be 1.024 meters high and unfortunately there are no buildings with such height in the world. [tex]\blacksquare[/tex]
The statement is incomplete, complete form is shown below:
A ball falls from the roof of a building and bounces half as high each time. How tall would a building have to be if, after hitting the ground ten times, the ball bounces to 1 meter? Is there a building this tall?
To learn more on geometric series, we kindly invite to check this verified question: https://brainly.com/question/15130111
