Looking for trustworthy answers? Westonci.ca is the ultimate Q&A platform where experts share their knowledge on various topics. Ask your questions and receive detailed answers from professionals with extensive experience in various fields. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
9514 1404 393
Answer:
7.51 m
Step-by-step explanation:
The distance traveled to the first floor hit is 1 m. The next hit has a height that is 14% less, so is 100% -14% = 86% = 0.86 times this height. The travel up and down to/from that height is added to the total.
The distance traveled to the second floor hit is 1 m + 2×(0.86×1 m).
The distance traveled to the third floor hit is 1 m + 0.86×2 m + 0.86²×2 m.
Then the distance traveled to the n-th floor hit is ...
-1 m + Sum(0.86^k × 2 m) for k = 0 to n-1
The sum can be found from the formula for the sum of a geometric series:
Sn = a1×(r^n -1)/(r-1) . . . . . where a1 is the first term and r is the common ratio.
For r = 0.86, n = 6, and a1 = (2m), the total distance is ...
vertical distance = -1 m + (2 m)(0.86^6 -1)/(0.86 -1)
= -1 m + (2 m)(-0.5954)/(-0.14) ≈ 7.5062 m
The total distance traveled to the 6th floor hit is about 7.51 meters.
_____
Alternate solution
Another way to answer the question is to add up the distances for each bounce. Attached is a spreadsheet that does that.

Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. We hope you found this helpful. Feel free to come back anytime for more accurate answers and updated information. We're glad you visited Westonci.ca. Return anytime for updated answers from our knowledgeable team.