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When a Cray-Ze-Ball is dropped, it bounces to half the height it was dropped from. If a Cray-Ze-Ball is dropped from a height of $6$ feet, how far has it traveled when it touches the ground the $5$th time?

 Jun 5, 2021
 #1
avatar+179 
0

The first time it hits the floor, it will have fallen 6ft.

 

The second time it hits the floor, it will have fallen 6ft, bounced up 3ft, and fallen 3ft.  

 

The third time it hits the floor, it will have fallen 6ft, bounced up 3ft, and fallen 3ft, bounced up 1.5 feet, and fallen 1.5 feet.  

 

The fourth time it hits the floor,  it will have fallen 6ft, bounced up 3ft, and fallen 3ft, bounced up 1.5 feet, and fallen 1.5 feet, bounced up 0.75 feet, and fallen 0.75 feet.  

 

The fifth time it hits the floor, it will have fallen 6ft, bounced up 3ft, and fallen 3ft, bounced up 1.5 feet, and fallen 1.5 feet, bounced up 0.75 feet, and fallen 0.75 feet, bounced up 0.375 feet, and fallen 0.375 feet.  Together, the total distance is 6+3+3+1.5+1.5+0.75+0.75+0.375+0.375 = 6+6+3+1.5+0.75 = 15 +2.25 = 17.25 feet.  

 

Hopefully, this answered your question, have a great day!

 Jun 5, 2021
 #2
avatar+121054 
+2

The total  distance  traveled  when the  ball hits the  groud for  the  nth time is

 

6 +  6  ( 1 - (1/2)^(n-1) )   / (1/2)

 

So.....when it  touches  the  ground for  the  5th time

 

6  +  6 (1 - (1/2)^4)  / (1/2)  =

 

6 + 12  ( 1 - 1/16)   =

 

6 +  12  ( 15/16)   =

 

17.25   ft 

 

 

cool cool cool

 Jun 5, 2021

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