To calculate:total vertical distance the ball travels before coming to rest.
Answer to Problem 90E
The total vertical distance the ball travels before rest is
Explanation of Solution
Given information:The height of each bounces is three − fourths the height of the previous bounce and graph
Formula needed:sum of infinite geometric sequence
Calculation:Initially, the vertical distance covered by ball is 6 feet i.e.,
After first bounce, the vertical distance covered by ball is two times of previous height i.e.,
After second bounce, the vertical distance covered by ball is two times of previous height i.e.,
After third bounce, the vertical distance covered by ball is two times of previous height i.e.,
And so on.
The nth bounce is given by
The total vertical distance is
Here,
Hence, the total vertical distance the ball travels before rest is
Chapter 9 Solutions
EBK PRECALCULUS W/LIMITS
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