Question

муха вылетела из Барнаула в Иркутск (2500 км) со скорость 1м/с. Она удваивает скорость после каждого метра пути. Оцените время полета мухи.

Answer 1

(Исправленное решение)

2 500 км=2 500 000 м

Значения скорости мухи после каждого метра есть последовательные члены геометрической прогресии с первым членом 1 и знаменателем 2.

Муха изменит свою скорость (2 500 000 - 1)= 2 499 999 раз пока долетит до Иркутска

Временный отрезки, за которое она преодолеет каждый следующий метр есть последовательные члены геометрической прогрессии с первым членом 1, и знаменателем 1\2   

2500км=2 500 000 м

Формула общего члена геометрической прогресии b[n]=b[1]*q^(n-1)

Сумма первых n членов геометричесской прогресии равна S[n]=(b[1]-b[n]*q)\(1-q)

 

b[1]=1 q=1\2 n=2 499 999

Время за которое муха одолеет последний метр

b[2 499 999]=1*(1\2)^(2 499 999-1)=(1\2)^2 499 998

Время за которое муха преодолеет свой путь

S[2 499 999]=(1-(1\2)^2 499 998*2)\(1-1\2)=2*(1-(1\2)^2 499 999)<2

Ответ:  меньше 2с

з.ы.шустрая муха

Answer 2

Calculation of Flight Time for the Fly

To calculate the flight time of the fly from Barnaul to Irkutsk, we need to consider the distance between the two cities and the fly's speed.

Given: - Distance from Barnaul to Irkutsk: 2500 km - Fly's initial speed: 1 m/s - Fly doubles its speed after each meter of the journey

To estimate the flight time, we can break down the fly's journey into smaller segments and calculate the time taken for each segment.

Let's calculate the time taken for the fly to cover each meter of the journey:

1. For the first meter, the fly's speed is 1 m/s. Therefore, it takes 1 second to cover the first meter.

2. After covering the first meter, the fly's speed doubles to 2 m/s. It will take 0.5 seconds to cover the second meter.

3. After covering the second meter, the fly's speed doubles again to 4 m/s. It will take 0.25 seconds to cover the third meter.

4. This pattern continues for each subsequent meter. The time taken to cover each meter will be halved compared to the previous meter.

To calculate the total flight time, we need to sum up the time taken for each meter of the journey.

Let's calculate the total flight time for the fly:

1 second (for the first meter) + 0.5 seconds (for the second meter) + 0.25 seconds (for the third meter) + ...

To simplify the calculation, we can use the formula for the sum of an infinite geometric series:

S = a / (1 - r)

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

In this case, the first term (a) is 1 second, and the common ratio (r) is 0.5 (since the time taken for each meter is halved compared to the previous meter).

Using the formula, we can calculate the total flight time:

S = 1 / (1 - 0.5) = 2 seconds

Therefore, the estimated flight time for the fly from Barnaul to Irkutsk is approximately 2 seconds.

Please note that this calculation assumes the fly maintains a constant doubling of speed after each meter of the journey. In reality, factors such as fatigue, environmental conditions, and other variables may affect the fly's actual flight time.