Question

Два автомобиля одновременно начали движение из точки а.Автомобили двигались в различных направлениях каждый по прямой дороге скорость первого автомобиля былa 90 км час скорость второго автомобиля 60 километров в час а угол между дорогами q=120° найдите расстояние между автомобилями через две минуты после выезда из точки а

Answer 1

Со скоростью 90 км/ч 1 автомобиль за 2 мин проехал
90/60*2=90/30=3 км.
Со скоростью 60 км/ч 2 автомобиль за 2 мир проехал
60/60*2=2 км.
По теореме косинусов
S^2=3^2+2^2-2*3*2*cos 120=
=9+4-12*(-1/2)=13+6=19
S=√19 км.

Answer 2

Problem Analysis

We are given that two cars start moving simultaneously from point A. The cars are moving in different directions along straight roads. The speed of the first car is 90 km/h, the speed of the second car is 60 km/h, and the angle between the roads is 120°. We need to find the distance between the cars after two minutes.

Solution

To find the distance between the cars after two minutes, we need to calculate the distance each car has traveled in that time.

Let's start by calculating the distance traveled by the first car. We know that the speed of the first car is 90 km/h. In two minutes (or 1/30th of an hour), the first car will travel:

Distance of the first car = Speed of the first car × Time = 90 km/h × (1/30) h

Next, let's calculate the distance traveled by the second car. We know that the speed of the second car is 60 km/h. In two minutes (or 1/30th of an hour), the second car will travel:

Distance of the second car = Speed of the second car × Time = 60 km/h × (1/30) h

Now, we have the distances traveled by both cars. To find the distance between the cars, we can use the law of cosines. The law of cosines states that in a triangle, the square of one side is equal to the sum of the squares of the other two sides minus twice the product of the lengths of those sides multiplied by the cosine of the included angle.

In our case, the distance between the cars is the side opposite the angle between the roads. Let's call this distance 'd'. Using the law of cosines, we have:

d^2 = (Distance of the first car)^2 + (Distance of the second car)^2 - 2 × (Distance of the first car) × (Distance of the second car) × cos(q)

where 'q' is the angle between the roads.

Finally, we can calculate the distance between the cars by taking the square root of 'd^2':

Distance between the cars = sqrt(d^2)

Let's calculate the distance between the cars using the given values.

Calculation

Using the given values: - Speed of the first car = 90 km/h - Speed of the second car = 60 km/h - Angle between the roads (q) = 120° - Time = 2 minutes = 1/30 hour

We can substitute these values into the formulas to calculate the distance between the cars.

Distance of the first car = 90 km/h × (1/30) h = 3 km

Distance of the second car = 60 km/h × (1/30) h = 2 km

Now, let's calculate the distance between the cars using the law of cosines:

d^2 = (3 km)^2 + (2 km)^2 - 2 × (3 km) × (2 km) × cos(120°)

Using the law of cosines, we can calculate the value of 'd^2'.

d^2 = 9 km^2 + 4 km^2 - 2 × 3 km × 2 km × cos(120°)

d^2 = 13 km^2 - 12 km^2 × cos(120°)

Now, let's calculate the value of 'd^2'.

d^2 = 13 km^2 - 12 km^2 × (-0.5)

d^2 = 13 km^2 + 6 km^2

d^2 = 19 km^2

Finally, let's calculate the distance between the cars by taking the square root of 'd^2'.

Distance between the cars = sqrt(19 km^2) ≈ 4.36 km

Answer

The distance between the cars after two minutes is approximately 4.36 km.

Explanation

Two cars started moving simultaneously from point A. The first car traveled a distance of 3 km, and the second car traveled a distance of 2 km. The angle between the roads is 120°. Using the law of cosines, we calculated the distance between the cars to be approximately 4.36 km.