Question

Два па­ро­хо­да вышли из порта, сле­дуя один на север, дру­гой на запад. Ско­ро­сти их равны со­от­вет­ствен­но 15 км/ч и 20 км/ч. Какое рас­сто­я­ние (в километрах) будет между ними через 2 часа?

Answer 1

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Answer 2

Problem Analysis

Two ships leave a port, one heading north and the other heading west. The speeds of the ships are 15 km/h and 20 km/h, respectively. We need to determine the distance between the two ships after 2 hours.

Solution

To find the distance between the two ships after 2 hours, we can use the concept of relative velocity. The relative velocity is the vector difference between the velocities of the two ships.

Let's assume the ship heading north is Ship A and the ship heading west is Ship B.

The velocity of Ship A is 15 km/h towards the north, and the velocity of Ship B is 20 km/h towards the west.

Since the ships are moving in perpendicular directions, we can use the Pythagorean theorem to find the distance between them.

The distance between the two ships after 2 hours can be calculated using the formula:

Distance = √((Distance_A)^2 + (Distance_B)^2)

where: - Distance_A = Velocity_A * Time - Distance_B = Velocity_B * Time

Let's calculate the distance between the two ships after 2 hours.

Calculation

Given: - Velocity_A = 15 km/h - Velocity_B = 20 km/h - Time = 2 hours

Using the formula above, we can calculate the distance between the two ships:

Distance_A = Velocity_A * Time = 15 km/h * 2 hours = 30 km

Distance_B = Velocity_B * Time = 20 km/h * 2 hours = 40 km

Distance = √((Distance_A)^2 + (Distance_B)^2) = √((30 km)^2 + (40 km)^2) = √(900 km^2 + 1600 km^2) = √(2500 km^2) = 50 km

Therefore, the distance between the two ships after 2 hours is 50 kilometers.

Answer

The distance between the two ships after 2 hours will be 50 kilometers.