A ball falls freely from the height of 100 meters, and bounces back to half of its original height after each landing; Fall again and ask how many meters * * * passed when landing for the first time 10. A ball falls freely from the height of 100 meters, and bounces back to half of its original height after each landing; Fall again, and ask it to pass 299.8 meters when landing for the first time 10.

Analysis and solutions:

After each landing, it bounces back to half the original height, and the distance traveled is half of the original height, that is, the original height is divided by 2.

First landing pass 100m, which is counted as a1;

The heading for the second landing is (100/2) * 2 = 100 m, which is counted as A2;

The third landing pass (100/4) * 2 = 50m, counted as A3;

The fourth landing is (100/8) * 2 = 25m, which is A4;

The nth landing pass [100/2 (n-1)] * 2 =100/2 (n-2), count as one;

10 Landing * * * Distance traveled:

S 10=a 1+a2+a3+？ +a 10 = 100+ 100+50+？ +100/2 8 = 299.6 meters.

Extended data:

1. Analyze the distance traveled by the ball every time it lands, including falling and bouncing.

For example, the first landing through 100 meters; After that, it bounced 50 meters and landed 50 meters. So the second landing passed 100 meters; Then it bounced back 25 meters and landed 25 meters. So I landed 50 meters for the third time; ? Summarize the law of the ball landing distance.

2. The total distance of10 landings needs to be obtained by adding the distances of each landing.