Question

Летящий горизонтально со скоростью 250м/с снаряд разрывается на два осколка, летящие в том же направлении. Скорость первого осколка 100м/с, а второго 300м/с. Чему равно отношение массы второго осколка к массе первого осколка?​

Answer 1

Ответ: 3

Объяснение: См. приложение

Answer 2

Projectile Motion and Conservation of Momentum

When a projectile explodes into two fragments, the conservation of momentum can be used to determine the relationship between the masses of the fragments. In this case, a projectile traveling horizontally at 250 m/s explodes into two fragments, one traveling at 100 m/s and the other at 300 m/s in the same direction.

Conservation of Momentum: The conservation of momentum states that the total momentum of an isolated system remains constant if no external forces act on it.

Calculating the Mass Ratio

To find the mass ratio of the two fragments, we can use the conservation of momentum equation:

Initial Momentum = Final Momentum

The initial momentum is the momentum of the original projectile, and the final momentum is the combined momentum of the two fragments.

The momentum (p) of an object is given by the product of its mass (m) and velocity (v): \[ p = m \times v \]

Using the conservation of momentum equation, we can set up the following relationship: \[ m_1 \times v_1 + m_2 \times v_2 = (m_1 + m_2) \times V \]

Where: - \( m_1 \) and \( v_1 \) are the mass and velocity of the first fragment - \( m_2 \) and \( v_2 \) are the mass and velocity of the second fragment - \( V \) is the velocity of the combined fragments

Applying the Given Values

Given: - Initial velocity of the projectile (u) = 250 m/s - Velocity of the first fragment (v1) = 100 m/s - Velocity of the second fragment (v2) = 300 m/s

We can use the equation to solve for the mass ratio of the two fragments.

Solution

Using the given values, we can solve for the mass ratio of the second fragment to the first fragment.

\[ m_1 \times 100 + m_2 \times 300 = (m_1 + m_2) \times 250 \]

Solving for the mass ratio: \[ 100m_1 + 300m_2 = 250m_1 + 250m_2 \] \[ 50m_1 = 50m_2 \] \[ m_1 = m_2 \]

Therefore, the mass of the second fragment is equal to the mass of the first fragment. The mass ratio of the second fragment to the first fragment is 1:1.