a.
To calculate : The distance does the ball travel between the first and second bounce and between second and third bounce.
The ball travels
Given information :
A student drops a rubber ball from a height of
Formula used :
Calculate the sum of total distance covered by ball between the consecutive bounces.
Calculation :
It can be observed that ball fell from a height of
After that it travels up for
The distance between first and second bounce for the ball is
From, the picture it can be seen that between second and third bounce the ball travels
The distance between second and third bounce for the ball is
Thus, the ball travels
b.
To calculate : The infinite series to model total distance travelled by the ball if the distance travelled before the first bounce is excluded.
The infinite series to model total distance travelled by the ball is
Given information :
A student drops a rubber ball from a height of
Formula used :
The
Calculation :
If the distance before first bounce is ignored, the ball travels distance of
So, total distance covered by the ball in the subsequent bounces can be written as follows.
Here the first term is
The geometric series is written as
Thus, the infinite series to model total distance travelled by the ball is
c.
To calculate : The distance travelled by the ball including the distance travelled before the first bounce.
The distance travelled by the ball including the distance travelled before the first bounce is
Given information :
A student drops a rubber ball from a height of
Formula used :
The sum of infinite geometric series with first term
Here,
Calculation :
The total distance travelled if the distance travelled before the first bounce included is
For the geometric series
So,
Thus, the distance travelled by the ball including the distance travelled before the first bounce is
d.
To prove : The distance travelled by the ball before the first bounce is
Given information :
A student drops a rubber ball from a height of
Formula used :
The sum of infinite geometric series with first term
Here,
Explanation :
If the distance covered is
For the geometric series
So,
Chapter 7 Solutions
Holt Mcdougal Larson Algebra 2: Student Edition 2012
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