Question

A basketball drops from a hieght of 76 in. On bounce 1, it rebounds to a hieght of 38 in. On bounce 2, it rebounds to a hieght of 19 in. How high does the basketball bounces on bounce 3

Answer 1

Answer:  The required height of the basketball on bounce 3 is 9.5 in.

Step-by-step explanation:  Given that a basketball drops from a height of 76 in. On bounce 1, it rebounds to a height of 38 in. and on bounce 2, it rebounds to a height of 19 in.

We are to find the height to which basketball bounces on bounce 3.

If we write the heights of the basketball in consecutive bounces (0, 1, 2, . . .), then it will form a sequence as follows :

76,  38,   19,   .   .   .  

We see the following pattern in the consecutive heights as follows :

$\dfrac{38}{76}=\dfrac{19}{38}=~~.~~.~~.~~=\dfrac{1}{2}.$

Therefore, the height of the basketball in bounce 3 will be half of the height of the basketball in bounce 2.

That is, the height to which basketball bounces on bounce 3 will be

$h_3=9\times\dfrac{1}{2}=9.5~\textup{in}.$

Thus, the required height of the basketball on bounce 3 is 9.5 in.

Answer 2

On bounce 3, the height is 9.5 in