Question

Снаряд, летевший горизонтально со скоростью 480 м/c, разорвался на два осколка равной массы. Один осколок полетел вертикально вверх со скоростью 400 м/c относительно Земли. Определить скорость другого осколка.

Answer 1

Problem Analysis

We are given a scenario where a projectile traveling horizontally at a speed of 480 m/s breaks into two fragments of equal mass. One fragment travels vertically upwards with a speed of 400 m/s relative to the Earth. We need to determine the speed of the other fragment.

Solution

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

Let's assume the mass of each fragment is m.

Before the explosion, the total momentum is the sum of the momentum of the horizontal projectile and the momentum of the vertical fragment. Since the horizontal projectile is traveling horizontally, its vertical momentum is zero. Therefore, the total momentum before the explosion is:

Total momentum before explosion = (mass of horizontal projectile) * (velocity of horizontal projectile) + (mass of vertical fragment) * (velocity of vertical fragment)

After the explosion, the total momentum is the sum of the momentum of the two fragments. Since the fragments have equal mass, the momentum of each fragment is equal. Therefore, the total momentum after the explosion is:

Total momentum after explosion = 2 * (mass of fragment) * (velocity of fragment)

According to the principle of conservation of momentum, the total momentum before the explosion is equal to the total momentum after the explosion. Therefore, we can equate the two expressions for total momentum and solve for the velocity of the other fragment.

Let's calculate the velocity of the other fragment.

Calculation

Given: - Velocity of the horizontal projectile = 480 m/s - Velocity of the vertical fragment = 400 m/s

Let's assume the mass of each fragment is m.

Using the principle of conservation of momentum, we can equate the total momentum before the explosion to the total momentum after the explosion:

(mass of horizontal projectile) * (velocity of horizontal projectile) + (mass of vertical fragment) * (velocity of vertical fragment) = 2 * (mass of fragment) * (velocity of fragment)

Substituting the given values:

(m) * (480 m/s) + (m) * (400 m/s) = 2 * (m) * (velocity of fragment)

Simplifying the equation:

480 m + 400 m = 2 * (velocity of fragment)

880 m = 2 * (velocity of fragment)

Dividing both sides by 2:

velocity of fragment = 440 m/s

Therefore, the speed of the other fragment is 440 m/s.

Answer

The speed of the other fragment is 440 m/s.