Question

Снаряд массой 100кг , летящий горизонтально вдоль железнодорожного пути со скоростью 500м м/c попадает в вагон с песком массой 10т и застревает в нем. Найти скорость вагона, если он двигался со скоростью 36 км/ч навстречу снаряду.

Answer 1

По закону сохранения импульса

M*V2-m*V1=(m+M)*V

V=(M*V2-m*V1)/(m+M)=(10 000*10-500*100)/10100=500/101=4,95 м/с

Answer 2

Problem Analysis

We are given a scenario where a projectile with a mass of 100 kg is flying horizontally along a railway track with a speed of 500 m/s. The projectile hits a wagon filled with sand, which has a mass of 10 tons (10,000 kg), and gets stuck in it. We need to find the velocity of the wagon if it was initially moving towards the projectile with a speed of 36 km/h.

Solution

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

Let's denote the velocity of the wagon before the collision as v_wagon and the velocity of the projectile before the collision as v_projectile. After the collision, the projectile gets stuck in the wagon, so their final velocity will be the same. Let's denote this final velocity as v_final.

The total momentum before the collision is given by the sum of the momentum of the wagon and the momentum of the projectile:

Total momentum before collision = momentum of wagon + momentum of projectile

The momentum of an object is calculated by multiplying its mass by its velocity:

Momentum = mass * velocity

Using this information, we can set up the equation for the total momentum before the collision:

m_wagon * v_wagon + m_projectile * v_projectile = (m_wagon + m_projectile) * v_final

where m_wagon is the mass of the wagon, m_projectile is the mass of the projectile, and v_final is the final velocity of both the wagon and the projectile after the collision.

Now, let's substitute the given values into the equation and solve for v_final:

m_wagon * v_wagon + m_projectile * v_projectile = (m_wagon + m_projectile) * v_final

10,000 kg * (36 km/h) + 100 kg * (500 m/s) = (10,000 kg + 100 kg) * v_final

Note: We need to convert the speed of the wagon from km/h to m/s to ensure consistent units.

Calculation

Let's calculate the final velocity of the wagon:

10,000 kg * (36,000 m/3,600 s) + 100 kg * (500 m/s) = (10,100 kg) * v_final

100,000,000 kg*m/s + 50,000 kg*m/s = 10,100 kg * v_final

100,050,000 kg*m/s = 10,100 kg * v_final

Dividing both sides of the equation by 10,100 kg:

v_final = 100,050,000 kg*m/s / 10,100 kg

v_final ≈ 9,900 m/s

Answer

The velocity of the wagon, after the projectile gets stuck in it, is approximately 9,900 m/s.