Question

два парохода начинают движение из одного и того же пункта и двигаются равномерно по прямым, пересекающимся под углом 60 градусов. скорость первого 60 км/ч, скорость второго 70 км/ч. вычислить на каком расстоянии они будут находится через 3 часа.

Answer 1

а надо на каком расстоянии они будут находиться друг от друга или просто сколько проедут?

если сколько проедут то 1)180 км 2)210 км

 

 

Answer 2

Problem Analysis

We have two ships starting from the same point and moving uniformly along straight lines that intersect at a 60-degree angle. The first ship has a speed of 60 km/h, and the second ship has a speed of 70 km/h. We need to calculate the distance between them after 3 hours.

Solution

To solve this problem, we can use the concept of relative velocity. The relative velocity of the second ship with respect to the first ship is the vector sum of their individual velocities. We can then calculate the distance between the two ships using the formula:

Distance = Relative Velocity × Time

Let's calculate the relative velocity and then use it to find the distance between the ships.

Calculation

The relative velocity can be calculated using the law of cosines. The formula is:

Relative Velocity = √(v1^2 + v2^2 - 2v1v2cosθ)

Where: - v1 = velocity of the first ship (60 km/h) - v2 = velocity of the second ship (70 km/h) - θ = angle between the two ships (60 degrees)

Let's substitute the values into the formula and calculate the relative velocity:

Relative Velocity = √((60^2) + (70^2) - 2(60)(70)cos60)

Calculating this expression gives us the relative velocity.

Now, we can use the relative velocity and the given time (3 hours) to calculate the distance between the ships using the formula:

Distance = Relative Velocity × Time

Substituting the values, we can find the distance.

Calculation Steps

1. Calculate the relative velocity using the formula mentioned above. 2. Multiply the relative velocity by the given time (3 hours) to find the distance between the ships.

Let's perform the calculations.

Calculation Results

1. Relative Velocity = 2. Distance = Relative Velocity × Time

Distance =

Therefore, after 3 hours, the two ships will be approximately kilometers apart.