Question

Снаряд массой 100кг , летящий горизонтально со скоростью 500м м/c попадает в вагон с песком массой 10т и застревает в нём.Какую скорость приобретает вагон со снарядом если он двигался навстречу снаряду со скоростью 36м/с?

Answer 1

Problem Analysis

We have a projectile with a mass of 100 kg flying horizontally with a velocity of 500 m/s. It hits a wagon filled with sand, which has a mass of 10 tons (10,000 kg), and gets stuck in it. The wagon was moving towards the projectile with a velocity of 36 m/s. We need to determine the velocity acquired by the wagon with the projectile after the collision.

Solution

To solve this problem, we can use 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.

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 of the object, and - v is the velocity of the object.

Before the collision, the momentum of the projectile is given by:

p1 = m1 * v1

where: - m1 is the mass of the projectile (100 kg), and - v1 is the velocity of the projectile (500 m/s).

The momentum of the wagon before the collision is given by:

p2 = m2 * v2

where: - m2 is the mass of the wagon (10,000 kg), and - v2 is the velocity of the wagon (36 m/s).

After the collision, the projectile gets stuck in the wagon, so their masses combine. The total mass after the collision is the sum of the masses of the projectile and the wagon:

m_total = m1 + m2

The velocity of the wagon with the projectile after the collision is given by:

v_final = (m1 * v1 + m2 * v2) / m_total

Substituting the given values into the equation, we can calculate the final velocity of the wagon with the projectile.

Calculation

Using the given values: - m1 = 100 kg (mass of the projectile), - v1 = 500 m/s (velocity of the projectile), - m2 = 10,000 kg (mass of the wagon), and - v2 = 36 m/s (velocity of the wagon),

we can calculate the final velocity of the wagon with the projectile using the equation:

v_final = (m1 * v1 + m2 * v2) / m_total

Substituting the values:

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

Simplifying the equation:

v_final = (50,000 kg·m/s + 360,000 kg·m/s) / 10,100 kg

v_final = 410,000 kg·m/s / 10,100 kg

v_final ≈ 40.594 m/s

Answer

The wagon with the projectile acquires a velocity of approximately 40.594 m/s after the collision.