Question

Снаряд массой 10 кг, летящий со скоростью 600 м/с, ударяет в неподвижную платформу с песком массой 2 т и застревает в песке. С какой скоростью станет двигаться платформа?

Answer 1

Импульс снаряда до удара: 10 · 600 = 6000 кг ·м/с
Импульс платформы до удара равен 0
Импульс платформы со снарядом после удара равен: (2000 + 10)V
По теореме о сохранении импульса: 2010V = 6000
V = 6000 : 2010 ≈ 2.985 ≈ 3(м/с)
Ответ: примерно 3м/с

Answer 2

Calculation of the Final Velocity of the Platform

To calculate the final velocity of the platform after the projectile hits it, 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. Therefore, we can write the equation:

Initial momentum = Final momentum

The initial momentum is the momentum of the projectile before the collision, and the final momentum is the combined momentum of the projectile and the platform after the collision.

Let's denote the mass of the projectile as m1, the initial velocity of the projectile as v1, the mass of the platform as m2, and the final velocity of the platform as v2.

The initial momentum of the projectile is given by m1 * v1.

The final momentum of the platform and the projectile is given by (m1 + m2) * v2.

Setting the initial momentum equal to the final momentum, we have:

m1 * v1 = (m1 + m2) * v2

Now, let's substitute the given values into the equation:

- Mass of the projectile, m1: 10 kg - Initial velocity of the projectile, v1: 600 m/s - Mass of the platform, m2: 2,000 kg

Substituting these values into the equation, we have:

10 kg * 600 m/s = (10 kg + 2,000 kg) * v2

Simplifying the equation:

6,000 kg·m/s = 2,010 kg * v2

Now, we can solve for v2:

v2 = 6,000 kg·m/s / 2,010 kg

Calculating the value:

v2 ≈ 2.99 m/s

Therefore, the platform will have a final velocity of approximately 2.99 m/s after the projectile hits it.