Question

Човен пливе через річку шириною s=500 м зі швидкістю відносно води v=5,2 м/с тримаючи курс під кутом a=30° до берега. Унаслідок зносу човна течією він припливає з точки А до точки С, яка знаходиться на відстані L=100м від точки В. Якою є швидкість u течії річки?​

Answer 1

Ответ: 5

Объяснение:

Фото

Answer 2

Problem Analysis

We are given the following information: - The boat is crossing a river with a width of s = 500 m. - The boat has a velocity relative to the water of v = 5.2 m/s. - The boat maintains a course at an angle of a = 30° to the shore. - Due to the current, the boat drifts from point A to point C, which is at a distance of L = 100 m from point B.

We need to find the velocity of the river current, u.

Solution

To solve this problem, we can use the concept of vector addition. The boat's velocity relative to the ground can be represented as the sum of its velocity relative to the water and the velocity of the river current.

Let's break down the boat's velocity relative to the ground into its horizontal and vertical components:

- The horizontal component of the boat's velocity relative to the ground is given by v * cos(a). - The vertical component of the boat's velocity relative to the ground is given by v * sin(a).

Since the boat is moving at a constant velocity, the horizontal component of the boat's velocity relative to the ground is equal to the velocity of the river current, u.

Therefore, we can write the equation:

u = v * cos(a)

Now, let's substitute the given values into the equation:

u = 5.2 m/s * cos(30°)

To calculate the value of cos(30°), we can use the trigonometric identity:

cos(30°) = sqrt(3) / 2

Substituting this value into the equation, we get:

u = 5.2 m/s * sqrt(3) / 2

Evaluating this expression, we find:

u ≈ 4.5 m/s

Answer

The velocity of the river current, u, is approximately 4.5 m/s.