Solve the problem.
-A ball is dropped from a height of $21 \mathrm {~m}$ and always rebounds $\frac { 1 } { 3 }$ of the height of the previous drop. How far does it travel (up and down) before coming to rest?
A) 42 m
B) 10.5 m
C) 63 m
D) 31.5 m

Question

Quizplus · Accepted Answer

The ball travels 21 m on the first drop, then $\frac { 1 } { 3 }$ of 21 m on the second drop, then $\frac { 1 } { 3 }$ of that on the third drop, and so on. The total distance traveled is the sum of this infinite geometric series:$$21 + 7 + 2.333... = 21 + \frac { 7 } { 1 - \frac { 1 } { 3 } } = 21 + \frac { 7 } { \frac { 2 } { 3 } } = 21 + 10.5 = 42 \mathrm {~m}$$

Solve the Problem 21 m21 \mathrm {~m}21 m And Always Rebounds 13\frac { 1 } { 3 }31​

Solve the Problem $21 \mathrm {~m}$ And Always Rebounds $\frac { 1 } { 3 }$