Final answer:
The ball dropped from an 8-meter building will travel a total distance of 24 meters before coming to rest, considering it bounces back half the height of the previous fall each time.
Step-by-step explanation:
The student is asking about the total distance traveled by a ball that is dropped from the top of an 8-meter building and bounces back up to half the drop height repeatedly until it comes to rest. To solve this problem, we can use a geometric series because each bounce is half the height of the previous one. When the ball is dropped, it travels 8 m downward. On the first bounce, it travels upward 4 m and then down again 4 m, and this pattern continues.
To find the total distance, we sum the infinite series: 8 + 2(4) + 2(2) + 2(1) + ... = 8 + 2(4 + 2 + 1 + ...) = 8 + 2(4/(1 - 1/2)) = 8 + 2(8) = 24 meters.
The total distance traveled by the ball before it comes to rest is 24 meters.