Question

Sandy dropped a basketball from the top of her Mom's office building which is 72 meters tall. She discovered that the ball bounced back 36 meters on the first bounce and 18 meters on the second bounce. If this pattern continues, how high will the ball be on the sixth bounce.

Answer 1

Answer:

1.125 m

Step-by-step explanation:

Given:

Initial height of the ball, $h_{0}=72\textrm{ m}$

Height after first bounce, $h_{1}=36\textrm{ m}$

Height after second bounce, $h_{2}=18\textrm{ m}$

So, the reduction in height after each bounce is half of the previous one. Thus, it follows a geometric sequence with the first term as 72 and common ratio of $r=\frac{1}{2}$.

Therefore, the nth term of a geometric sequence is given as:

$h_{n}=h_{0}r^{n}$

Here, $n=6,r=\frac{1}{2},h_{0}=72$. This gives,

$h_{6}=72\times (\frac{1}{2})^{6}\\h_{6}=\frac{72}{64}=1.125\textrm{ m}$.

Therefore, the height of the ball after sixth bounce is 1.125 m.