A Ball Drops from a Height of 6 Ft $\frac { 2 } { 5 }$

Multiple Choice

A ball drops from a height of 6 ft. With each bounce, the ball rebounds to $\frac { 2 } { 5 }$ of its height. The total vertical distanced traveled is given by $6 + 6 \left( \frac { 2 } { 5 } \right) + 2 ( 6 ) \left( \frac { 2 } { 5 } \right) ^ { 2 } + \ldots$ After the first term, the series is an infinite geometric series. Compute the total vertical distance traveled.

A) The total vertical distance traveled is 10 ft.
B) The total vertical distance traveled is 14 ft.
C) The total vertical distance traveled is 4 ft.
D) The total vertical distance traveled is 8 ft.