Question

Рыбак, сидя в лодке, отталкивается от бревна, которое при этом начинает двигаться со скорость 2 м/с какую скорость при этом приобретает лодка, если ее масса вместе с рыбаком в 4 раза больше массы бревна. Решите по закону сохранения импульсов или по 3 закону ньютона...

Answer 1

Используйте закон сохранения импульса: 

Answer 2

Problem Analysis

A fisherman sitting in a boat pushes off from a log, causing the log to move with a speed of 2 m/s. The mass of the boat, including the fisherman, is 4 times greater than the mass of the log. We need to calculate the speed acquired by the boat.

Solution

To solve this problem, we can use the law of conservation of momentum. According to this law, the total momentum before the interaction is equal to the total momentum after the interaction.

The momentum of an object is given by the product of its mass and velocity. Mathematically, momentum (p) is defined as:

p = m * v

Where: - p is the momentum of the object, - m is the mass of the object, and - v is the velocity of the object.

Let's assume the mass of the log is m1 and the mass of the boat (including the fisherman) is m2. The initial velocity of the log is v1 (0 m/s) and the final velocity of the log is v1' (2 m/s). The initial velocity of the boat is v2 (0 m/s) and the final velocity of the boat is v2'.

According to the law of conservation of momentum, the total momentum before the interaction is equal to the total momentum after the interaction:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

We are given that the mass of the boat (including the fisherman) is 4 times greater than the mass of the log:

m2 = 4 * m1

Substituting this into the equation, we have:

m1 * v1 + 4 * m1 * v2 = m1 * v1' + 4 * m1 * v2'

Simplifying the equation, we get:

v1 + 4 * v2 = v1' + 4 * v2'

Since the initial velocity of the log (v1) and the initial velocity of the boat (v2) are both 0 m/s, the equation becomes:

4 * v2 = v1' + 4 * v2'

We are asked to find the speed acquired by the boat, which is the final velocity of the boat (v2'). Solving the equation for v2', we get:

v2' = 4 * v2 - v1'

Substituting the given values, v2 = 0 m/s and v1' = 2 m/s, we can calculate the speed acquired by the boat:

v2' = 4 * 0 - 2 = -2 m/s

The negative sign indicates that the boat moves in the opposite direction to the log. Therefore, the speed acquired by the boat is 2 m/s in the opposite direction.

Answer

The boat, including the fisherman, acquires a speed of 2 m/s in the opposite direction when the fisherman pushes off from the log.

Explanation

When the fisherman pushes off from the log, the law of conservation of momentum states that the total momentum before the interaction is equal to the total momentum after the interaction. Since the initial velocity of the log is 0 m/s and the final velocity of the log is 2 m/s, the boat acquires a speed of 2 m/s in the opposite direction to the log.