Question

The height a ball bounces is less than the height of the previous bounce due to friction. The heights of the bounces form a geometric sequence. Suppose a ball is dropped from one meter and rebounds to 95% of the height of the previous bounce. What is the total distance travel by the ball when it comes to rest?
*Does the problem give you enough information to solve the problem?
*How can you write the general term of the sequence?
*What formula should you use to calculate the total distance?

Answer 1

@Data_LG2

Answer 2

so the series is

\(1+0.95(1) + 0.95^2+0.95^3.......)

Answer 3

okay what would the general term of the sequence?

Answer 4

so \(\sum_0^\infty (0.95)^n\)

Answer 5

okay what is the total distance then??

Answer 6

The sum of a geometric series with ratio less than one is given by \(\frac{a}{1-r}\) where \(a\) is the first term, and \(r\) is the common ratio.

Answer 7

wait
it would be

1+2(.95)+2(.95)(.95).....

Answer 8

2*.95^1+2*.95^2+...+2*.95^inifinity which is = to
-(2*.95)/(.95-1)=38

+ 1 :P which is the initial drop =39

Answer 9

right?

Answer 10

it would be \(1+2\sum_1^\infty (0.95)^n\)

Answer 11

I get 39

Answer 12

good job