The ball has travelled a total distance of 18 feet after dropping and rebounding.
After being dropped for the first time, the ball will rebound to a height of 3 feet as it returns to half its original height. The geometric series formed by the total distance travelled while falling and rebounding has a common ratio,
r = 0.5
6 ft + 3 ft = 9 ft will be the first term in the series
For the sum formula S = [tex]\frac{a}{1-r}[/tex],
substitute a = 9 and r = 0.5 to get the ball's total distance travelled.
S = [tex]\frac{9}{1-0.5}[/tex]
S = [tex]} \frac{9}{0.5}[/tex]
S = 18
The ball has therefore travelled a total of 18 feet.
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