Question

Стараясь равномерно грести перпендикулярно течению (v' const) пловец переплывает реку шириной 20 метров за 5 минут. Какова скорость течения реки u, если пловец проделал путь 50 метров

Answer 1

Запишем систему уравнений: (Корень из v0^2 + v^2)*t=S v0t=H; Где v0-скорость пловца, v-скорость течения, S-путь, Н-ширина реки; Из второго уравнения находим, что скорость пловца равна 1/15; Из первого уравнения находим скорость течения, которая равна: Корень из S^2/t^2-v0^2=0.153 м/с

Answer 2

Problem Analysis

We are given that a swimmer crosses a river with a width of 20 meters in 5 minutes by swimming perpendicular to the current. We need to find the speed of the river current.

Solution

Let's assume the speed of the swimmer relative to the water is v and the speed of the river current is u. Since the swimmer is swimming perpendicular to the current, the resultant velocity of the swimmer will be the vector sum of the swimmer's velocity and the river current velocity.

The swimmer's velocity relative to the ground can be calculated using the Pythagorean theorem:

v^2 = (v' + u)^2 + v'^2

where v' is the speed of the swimmer relative to the water.

We are given that the swimmer crosses a distance of 50 meters in 5 minutes. We can use this information to find the value of v':

v' = distance / time = 50 meters / 5 minutes = 10 meters per minute

Now, we can substitute the value of v' into the equation above:

v^2 = (10 + u)^2 + 10^2

Simplifying the equation:

v^2 = 100 + 20u + u^2 + 100

v^2 = u^2 + 20u + 200

Since the swimmer is swimming perpendicular to the current, the resultant velocity v is equal to the speed of the swimmer relative to the ground. We are given that the swimmer crosses a distance of 50 meters, so we can write:

v = distance / time = 50 meters / 5 minutes = 10 meters per minute

Substituting this value into the equation:

10^2 = u^2 + 20u + 200

Simplifying the equation:

100 = u^2 + 20u + 200

Rearranging the equation:

u^2 + 20u + 100 = 0

This is a quadratic equation. We can solve it by factoring or using the quadratic formula. Let's use the quadratic formula:

u = (-b ± √(b^2 - 4ac)) / (2a)

In this case, a = 1, b = 20, and c = 100. Substituting these values into the formula:

u = (-20 ± √(20^2 - 4 * 1 * 100)) / (2 * 1)

Simplifying the equation:

u = (-20 ± √(400 - 400)) / 2

u = (-20 ± √0) / 2

u = -20 / 2

u = -10

Since the speed of the river current cannot be negative, we discard the negative solution. Therefore, the speed of the river current is u = 10 meters per minute.

Answer

The speed of the river current is 10 meters per minute.