Question

Напишите подробное решение: Пловец переплывает реку по прямой, перпендикулярной берегу. Во сколько раз числовое значение скорости пловца относительно воды больше скорости течения, если угол между векторами скорости пловца относительно воды и относительно берега равен 30°. Ответ:2

Answer 1

30:15=2 , Смотри объяснение ниже.

Объяснение:

течение воды идет к берегу,туда плывет пловец.Это равно 30 градусов,сам плавец плывет под углом вектора 15 градусов.Это мы разделяем 30:15,в итоге 2.

Answer 2

Problem Analysis

We are given that a swimmer is crossing a river in a straight line perpendicular to the shore. We need to determine the ratio of the swimmer's speed relative to the water to the speed of the river current, given that the angle between the swimmer's velocity vector relative to the water and the velocity vector relative to the shore is 30°.

Solution

Let's assume the swimmer's speed relative to the water is represented by Vw and the speed of the river current is represented by Vc. We need to find the ratio Vw / Vc.

To solve this problem, we can use the concept of vector addition. The swimmer's velocity relative to the shore is the vector sum of the swimmer's velocity relative to the water and the velocity of the river current.

Let's consider the following diagram:

         Vw
        ------>
        ------>
       /       /
      /       /
     /       /
    /       /
   /       /
  /       /
 /       /
/       /
------> Vc

In this diagram, the swimmer's velocity relative to the water (Vw) is shown as an arrow pointing to the right, and the velocity of the river current (Vc) is shown as an arrow pointing downwards.

The angle between Vw and Vc is given as 30°. Since the swimmer is crossing the river in a straight line perpendicular to the shore, the angle between Vw and the shore is also 30°.

Using the concept of vector addition, we can find the swimmer's velocity relative to the shore (Vs) by adding Vw and Vc as vectors. The magnitude of Vs can be found using the law of cosines:

|Vs|^2 = |Vw|^2 + |Vc|^2 - 2|Vw||Vc|cos(30°)

Since we are interested in the ratio Vw / Vc, we can divide both sides of the equation by |Vc|^2:

(|Vs|^2) / (|Vc|^2) = (|Vw|^2) / (|Vc|^2) + 1 - 2(|Vw| / |Vc|)cos(30°)

Simplifying the equation, we get:

(Vw / Vc)^2 - 2(Vw / Vc)cos(30°) + 1 = 0

This is a quadratic equation in terms of Vw / Vc. Solving this equation will give us the desired ratio.

Using the quadratic formula, we have:

(Vw / Vc) = (2cos(30°) ± √(4cos^2(30°) - 4)) / 2

Simplifying further, we get:

(Vw / Vc) = cos(30°) ± √(cos^2(30°) - 1)

Since we are looking for a positive ratio, we take the positive square root:

(Vw / Vc) = cos(30°) + √(cos^2(30°) - 1)

Now, we can substitute the value of cos(30°) into the equation:

(Vw / Vc) = (√3 / 2) + √((√3 / 2)^2 - 1)

Simplifying further, we get:

(Vw / Vc) = (√3 / 2) + √(3 / 4 - 1) (Vw / Vc) = (√3 / 2) + √(-1 / 4) (Vw / Vc) = (√3 / 2) + (√-1 / 2) (Vw / Vc) = (√3 / 2) + (i / 2)

Therefore, the ratio of the swimmer's speed relative to the water to the speed of the river current is (√3 / 2) + (i / 2).

Answer

The ratio of the swimmer's speed relative to the water to the speed of the river current, given that the angle between the swimmer's velocity vector relative to the water and the velocity vector relative to the shore is 30°, is (√3 / 2) + (i / 2).

Note: The answer is a complex number because the square root of a negative number is involved in the calculation.