Question

Ахиллес бежит за черепахой со скоростью 3 м/с. между ними 100 м. на какой по счету секунде Ахиллес догонит черепаху, которая ползет в 100 раз медленнее,чем бежит Ахиллес?

Answer 1

1) скорость черепахи 3/100 м/с
2) 3-3/100=2 93/100 м/с - скорость сближения Ахиллеса и черепахи.
3)100м/2 93/100=34.13
Ответ: Ахиллес догонит ее на 35 секунде

Answer 2

Calculating When Achilles Will Catch the Tortoise

To calculate when Achilles will catch the tortoise, we can use the concept of infinite series and the formula for the sum of an infinite geometric series. The distance between them is 100 meters, and the tortoise moves at 1/100th of Achilles' speed, or 0.03 m/s.

Using the formula for the sum of an infinite geometric series, we can calculate the time it takes for Achilles to catch the tortoise.

The formula for the sum of an infinite geometric series is:

S = a / (1 - r)

Where: - S is the sum of the series - a is the first term - r is the common ratio

In this case, the first term a is the initial distance between Achilles and the tortoise (100 meters), and the common ratio r is the ratio of the tortoise's speed to Achilles' speed (0.03 m/s / 3 m/s = 1/100).

Calculating the Time

Using the formula, we can calculate the time it takes for Achilles to catch the tortoise:

S = 100 / (1 - 1/100)

S = 100 / (99/100)

S = 100 * (100/99)

S ≈ 100.01 meters

So, Achilles will catch the tortoise after approximately 100.01 meters.

Now, let's convert this distance into time using the given speeds of Achilles and the tortoise.

Converting Distance to Time

To convert the distance into time, we can use the formula:

time = distance / speed

For Achilles: time = 100.01 meters / 3 m/s

time ≈ 33.34 seconds

Therefore, Achilles will catch the tortoise on approximately the 34th second.