Question

Катер прошел по озеру в направлении точно на северо восток 2 км, а затем еще 1 км на север. Найти графически модуль и направление вектора перемещения

Answer 1

Модуль=корень из 2^2+1^2-2cos135град=корень из 7,83 примерно это будет 2,7 км

Answer 2

Problem Analysis

A boat traveled on a lake in a specific direction. It first traveled 2 km in the northeast direction and then an additional 1 km to the north. We need to find the graphical representation, magnitude, and direction of the displacement vector.

Solution

To find the graphical representation of the displacement vector, we can draw a diagram. Let's assume that the starting point of the boat is the origin (0,0) on a coordinate plane.

The boat first traveled 2 km in the northeast direction. This means it moved 2 km to the right (east) and 2 km up (north) from the starting point. We can represent this movement as a vector with components (2, 2).

Next, the boat traveled an additional 1 km to the north. This means it moved 1 km up (north) from its current position. We can represent this movement as a vector with components (0, 1).

To find the displacement vector, we can add these two vectors together. Adding the components, we get (2+0, 2+1) = (2, 3).

Magnitude of the Displacement Vector

The magnitude of a vector can be found using the Pythagorean theorem. The magnitude of the displacement vector is the square root of the sum of the squares of its components.

In this case, the magnitude of the displacement vector is √(2^2 + 3^2) = √(4 + 9) = √13 ≈ 3.61 km.

Direction of the Displacement Vector

The direction of the displacement vector can be found using trigonometry. We can calculate the angle between the displacement vector and the positive x-axis.

In this case, the angle can be found using the arctan function: arctan(3/2) ≈ 56.31 degrees.

Therefore, the direction of the displacement vector is approximately 56.31 degrees north of east.

Summary

The graphical representation of the displacement vector can be represented as a vector with components (2, 3). The magnitude of the displacement vector is approximately 3.61 km, and the direction is approximately 56.31 degrees north of east.

Please note that the values provided in this response are based on the given information and calculations.