A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 3 years ago
On average, when a basketball is dropped, it bounces 7/10 as high as it did on the previous bounce. If a ball is dropped from a height of 10 m, determine the total distance up and down that the ball travels by top of the 11th bounce. Round to the nearest hundredth
 3 years ago
On average, when a basketball is dropped, it bounces 7/10 as high as it did on the previous bounce. If a ball is dropped from a height of 10 m, determine the total distance up and down that the ball travels by top of the 11th bounce. Round to the nearest hundredth

This Question is Closed

dumbcow
 3 years ago
Best ResponseYou've already chosen the best response.0it is the sum of a geometric sequence Sum = 10[(1.7^11)/(1.7)] = 32.67

Jemurray3
 3 years ago
Best ResponseYou've already chosen the best response.0Are you familiar with the sum of a geometric series? Let \[S = 1 + x + x^2 + x^3 +...+x^n\] then \[xS = x + x^2 + x^3 + ...+x^{n+1}\] and so \[S  xS = S(1x) = 1  x^{n+1}\] So \[S = \frac{1x^{n+1}}{1x}\] That's the sum of a geometric series. Now examining your problem, we have to add the following: \[ 10 + \frac{7}{10} \cdot 10 + \frac{7}{10}\cdot 10 + \left(\frac{7}{10}\right)^2 \cdot 10 + \left(\frac{7}{10}\right)^2 \cdot 10 + ... \] so on and so forth. Noting that the distance traveled (oneway, either up or down) after the nth bounce is \[\left(\frac{7}{10}\right)^n \cdot 10\] and that everything except the first and last bounce is repeated, we can say that our total distance traveled is \[\left[2\sum_{n=0}^{11} \left(\frac{7}{10}\right)^n\cdot 10\right] 10  \left(\frac{7}{10}\right)^{11}\cdot 10\] but this looks just like a geometric series with x = 7/10, so that means \[\sum_{n=0}^{11} \left(\frac{7}{10}\right)^n = \frac{1\left(\frac{7}{10}\right)^{12}}{1\frac{7}{10}}\] And the rest is just calculation... :)
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.