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Hi, I know Im not suppsoed to do 2 questions per forum however I dont know the difference between these two problems and why the calculation process at the end is different from each other.

 

1) A tennis ball is shot vertically to a height of 20 feet and aloowed to drop. Each bounce is 80% as high as the previous bounce. What is the total distance the ball travels from when it is shot unit it bounces the fourth time?

 

2) Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. What is the total distance the ball traveled.

 May 22, 2022
 #1
avatar+117494 
+1

Hi Jenny

 

1) A tennis ball is shot vertically to a height of 20 feet and aloowed to drop. Each bounce is 80% as high as the previous bounce. What is the total distance the ball travels from when it is shot unit it bounces the fourth time?

0.8*20=16

0.8*16=12.8  

etc

so 

Up distance = 20+16+12.8+.....    sum to infinity

down distance = 20+16+12.8+ ....sum to infinity

add them together

 

 

2) Suppose you drop a tennis ball from a height of 15 feet. After the ball hits the floor, it rebounds to 85% of its previous height. What is the total distance the ball traveled.

15*0.85=12.75

12.65*0.85=10.8375

down distance = 15+12.75+10.8375+ ... sum to infinity

up distance = 12.75+10.8375+.... sum to infinity

add them together

 

use GP sum of infinite series to get the first answers.

 

Is that enough help?

 May 22, 2022
 #2
avatar+612 
+1

yes thank you I understand it a lot better now smiley

 May 22, 2022
 #3
avatar+117494 
+1

Very glad to hear it     cool

Melody  May 22, 2022

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