Question

Лодочник переправляясь через реку направил лодку под углом Ф=45* к направлению течения. В стоячей воде лодка движется со скоростью 3 м/с.Скорость течения реки 1 м/с.Определить абсолютную скорость движения лодки, а также время в течении которого лодка переплывёт реку шириной l= 360 м.

Answer 1

1 найдем составляющую скорости лодки перпендикулярно скорости реки

Vy=Vo*sin45=3*0,7=2,1м/с
2 Найдем время переправы  t=L/Vy=360/2,1=171.4 c
3 найдем составляющую скорости лодки Vx=Vo*cos45=2,1 м/с
Vx+Vp=2,1+1=3,1 м\с
найдем скорость лодки относительно берега  V= корень из 14,02=3,74м/с

Answer 2

Problem Analysis

We are given the following information: - The boatman is crossing a river with a boat. - The boat is directed at an angle of 45 degrees to the direction of the current. - The boat moves with a speed of 3 m/s in still water. - The speed of the river current is 1 m/s. - The width of the river is 360 m.

We need to determine the absolute velocity of the boat and the time it takes for the boat to cross the river.

Solution

To solve this problem, we can use vector addition to find the absolute velocity of the boat and then use the formula for time to calculate the time it takes to cross the river.

Let's break down the solution into steps:

1. Find the horizontal and vertical components of the boat's velocity. 2. Use the horizontal component of the boat's velocity to find the absolute velocity of the boat. 3. Use the vertical component of the boat's velocity to find the time it takes to cross the river.

Step 1: Find the horizontal and vertical components of the boat's velocity

The horizontal component of the boat's velocity is the component that is parallel to the direction of the current. It can be found using the formula:

V_horizontal = V_boat * cos(θ)

where: - V_horizontal is the horizontal component of the boat's velocity, - V_boat is the speed of the boat in still water (given as 3 m/s), - θ is the angle between the boat's direction and the direction of the current (given as 45 degrees).

The vertical component of the boat's velocity is the component that is perpendicular to the direction of the current. It can be found using the formula:

V_vertical = V_boat * sin(θ)

where: - V_vertical is the vertical component of the boat's velocity, - V_boat is the speed of the boat in still water (given as 3 m/s), - θ is the angle between the boat's direction and the direction of the current (given as 45 degrees).

Let's calculate the horizontal and vertical components of the boat's velocity:

Horizontal component: V_horizontal = 3 m/s * cos(45 degrees)

Vertical component: V_vertical = 3 m/s * sin(45 degrees)

Step 2: Use the horizontal component of the boat's velocity to find the absolute velocity of the boat

The absolute velocity of the boat is the resultant velocity obtained by adding the velocity of the boat in still water to the velocity of the river current. Since the horizontal component of the boat's velocity is parallel to the direction of the current, the absolute velocity of the boat will have the same magnitude as the horizontal component of the boat's velocity.

Therefore, the absolute velocity of the boat is:

V_absolute = V_horizontal

Step 3: Use the vertical component of the boat's velocity to find the time it takes to cross the river

The time it takes for the boat to cross the river can be found using the formula:

Time = Distance / V_vertical

where: - Time is the time it takes to cross the river, - Distance is the width of the river (given as 360 m), - V_vertical is the vertical component of the boat's velocity.

Let's calculate the time it takes to cross the river:

Time = 360 m / V_vertical

Now, let's calculate the values:

Horizontal component: V_horizontal = 3 m/s * cos(45 degrees) = 3 m/s * 0.7071 = 2.1213 m/s

Vertical component: V_vertical = 3 m/s * sin(45 degrees) = 3 m/s * 0.7071 = 2.1213 m/s

Absolute velocity of the boat: V_absolute = V_horizontal = 2.1213 m/s

Time to cross the river: Time = 360 m / V_vertical = 360 m / 2.1213 m/s = 169.7066 seconds

Therefore, the absolute velocity of the boat is 2.1213 m/s and it will take approximately 169.7066 seconds to cross the river.

Please let me know if I can help you with anything else.