Question

Платформа масою 100 кг рухається з певною швидкістю. Спортсмен масою 60 кг наздоганяє платформу та стрибає на неї, унаслідок чого швидкість руху платформи досягає 3 м/с. Визначте початкову швидкість руху платформи, якщо швидкість спортсмена в момент стрибка становила 4 м/с.​

Answer 1

Ответ:

2,8 м/с

Объяснение:

це точно правильно

Answer 2

Problem Analysis

We are given that a platform with a mass of 100 kg is moving at a certain velocity. A sportsman with a mass of 60 kg catches up to the platform and jumps onto it, causing the velocity of the platform to reach 3 m/s. We need to determine the initial velocity of the platform if the velocity of the sportsman at the moment of the jump is 4 m/s.

Solution

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

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, m is the mass, and v is the velocity.

Before the jump, the total momentum is the sum of the momentum of the platform and the momentum of the sportsman. After the jump, the total momentum is the sum of the momentum of the platform with the sportsman on it.

Let's denote the initial velocity of the platform as v1 and the final velocity of the platform after the jump as v2. The velocity of the sportsman before the jump is v3, and the velocity of the sportsman after the jump is v4.

According to the conservation of momentum, we can write the following equation:

m1 * v1 + m3 * v3 = (m1 + m3) * v2

where m1 is the mass of the platform, m3 is the mass of the sportsman, and v2 is the final velocity of the platform.

We are given the following values: - m1 (mass of the platform) = 100 kg - m3 (mass of the sportsman) = 60 kg - v3 (velocity of the sportsman before the jump) = 4 m/s - v2 (final velocity of the platform after the jump) = 3 m/s

Substituting these values into the equation, we can solve for v1:

100 kg * v1 + 60 kg * 4 m/s = (100 kg + 60 kg) * 3 m/s

Simplifying the equation:

100 kg * v1 + 240 kg * m/s = 160 kg * m/s

100 kg * v1 = 160 kg * m/s - 240 kg * m/s

100 kg * v1 = -80 kg * m/s

Dividing both sides of the equation by 100 kg:

v1 = -0.8 m/s

Therefore, the initial velocity of the platform is -0.8 m/s.

Note: The negative sign indicates that the platform was initially moving in the opposite direction of the sportsman's jump.