Question

A ball is dropped from a height of 6ft. whenever it hits the ground it bounces back to half its original height. what is the total distance the ball travels dropping and rebounding?

Answer 1

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 = $\frac{a}{1-r}$,  

substitute a = 9 and r = 0.5 to get the ball's total distance travelled.

S = $\frac{9}{1-0.5}$

S = $} \frac{9}{0.5}$

S = 18

The ball has therefore travelled a total of 18 feet.

Learn more about rebounding of ball here;

brainly.com/question/12848631

#SPJ4