Question

2. Вертолет пролетел по ветру расстояние 120 км и обратно вернулся, потратив на весь путь 8 час. Найдите скорость ветра, если скорость в штиль составляет 40 км/час.​

Answer 1

Объяснение:

скорость вертолёта по ветру- x

в штиль-40км/ч

S=120км

Answer 2

Problem Analysis

We are given that a helicopter flew a distance of 120 km against the wind and then returned, taking a total of 8 hours for the entire trip. We need to find the speed of the wind, given that the speed of the helicopter in calm conditions is 40 km/h.

Solution

Let's assume the speed of the wind is x km/h.

When the helicopter flies against the wind, its effective speed is reduced by the speed of the wind. Therefore, the time taken to cover the distance of 120 km against the wind can be calculated as:

Time against the wind = Distance / (Speed of helicopter - Speed of wind)

Similarly, when the helicopter flies with the wind, its effective speed is increased by the speed of the wind. Therefore, the time taken to cover the distance of 120 km with the wind can be calculated as:

Time with the wind = Distance / (Speed of helicopter + Speed of wind)

We are given that the total time for the entire trip is 8 hours. Therefore, the sum of the time against the wind and the time with the wind should be equal to 8 hours:

Time against the wind + Time with the wind = 8 hours

Now we can substitute the values and solve for the speed of the wind.

Calculation

Let's calculate the time against the wind and the time with the wind using the given values:

Time against the wind = 120 km / (40 km/h - x km/h)

Time with the wind = 120 km / (40 km/h + x km/h)

Since the total time is 8 hours, we have the equation:

120 km / (40 km/h - x km/h) + 120 km / (40 km/h + x km/h) = 8 hours

Now we can solve this equation to find the value of x, which represents the speed of the wind.

Solution

To solve the equation, we can multiply both sides by (40 km/h - x km/h) * (40 km/h + x km/h) to eliminate the denominators:

120 km * (40 km/h + x km/h) + 120 km * (40 km/h - x km/h) = 8 hours * (40 km/h - x km/h) * (40 km/h + x km/h)

Simplifying the equation:

120 km * (40 km/h + x km/h) + 120 km * (40 km/h - x km/h) = 8 hours * (40^2 km^2/h^2 - x^2 km^2/h^2)

Expanding and simplifying further:

4800 km^2/h + 120 km * x km/h + 4800 km^2/h - 120 km * x km/h = 3200 km^2/h^2 - 8 x^2 km^2/h^2

Combining like terms:

9600 km^2/h = 3200 km^2/h^2 - 8 x^2 km^2/h^2

Rearranging the equation:

8 x^2 km^2/h^2 + 9600 km^2/h - 3200 km^2/h^2 = 0

Dividing through by 8 km^2/h^2:

x^2 + 1200 km^2/h - 400 km^2/h^2 = 0

Now we have a quadratic equation in terms of x. We can solve this equation to find the value of x, which represents the speed of the wind.

Using the quadratic formula:

x = (-b ± √(b^2 - 4ac)) / (2a)

where a = 1, b = 1200 km^2/h, and c = -400 km^2/h^2.

Substituting the values:

x = (-1200 km^2/h ± √((1200 km^2/h)^2 - 4 * 1 * -400 km^2/h^2)) / (2 * 1)

Simplifying further:

x = (-1200 km^2/h ± √(1440000 km^4/h^2 + 1600 km^4/h^2)) / 2

x = (-1200 km^2/h ± √(1441600 km^4/h^2)) / 2

x = (-1200 km^2/h ± 1200 km^2/h) / 2

Now we have two possible values for x:

x1 = (-1200 km^2/h + 1200 km^2/h) / 2 = 0 km/h

x2 = (-1200 km^2/h - 1200 km^2/h) / 2 = -1200 km^2/h

Since the speed of the wind cannot be negative, the only valid solution is x = 0 km/h. This means that there is no wind.

Answer

Therefore, the speed of the wind is 0 km/h.