Question

Ядро, летевшее со скоростью 500 м/с, разорвалось на два осколка массами 5 и 15 кг. Скорость большего осколка, продолжавшего двигаться в том же направлении, стала равной 800 м/с. Определите скорость меньшего осколка (модуль и направление).

Answer 1

Mv=m1*v1+m2*v (15+5)*500=5*v1+15*800 v1=-2000/5=-400м.с минус указывает на то, что осколок летит в противоположную сторону от первоначального ядра.

Answer 2

Problem Analysis

We are given that a core, traveling at a speed of 500 m/s, has split into two fragments with masses of 5 kg and 15 kg. The larger fragment continues to move in the same direction and now has a speed of 800 m/s. We need to determine the speed of the smaller fragment, including its magnitude and direction.

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.

The momentum of an object is defined as the product of its mass and velocity. Mathematically, momentum (p) is given by the equation:

p = m * v

where p is the momentum, m is the mass, and v is the velocity.

Let's denote the mass of the smaller fragment as m1 and its velocity as v1. Similarly, let's denote the mass of the larger fragment as m2 and its velocity as v2.

Before the explosion, the total momentum is given by:

p_initial = m1 * v1 + m2 * v2

After the explosion, the total momentum is still conserved and is given by:

p_final = m1 * v1' + m2 * v2'

where v1' and v2' are the velocities of the smaller and larger fragments after the explosion, respectively.

Since the total momentum is conserved, we can equate the initial and final momenta:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

We are given the following information: - Mass of the smaller fragment (m1) = 5 kg - Mass of the larger fragment (m2) = 15 kg - Velocity of the larger fragment after the explosion (v2') = 800 m/s

We need to find the velocity of the smaller fragment after the explosion (v1').

To solve for v1', we rearrange the equation as follows:

m1 * v1 + m2 * v2 = m1 * v1' + m2 * v2'

v1' = (m1 * v1 + m2 * v2 - m2 * v2') / m1

Now, let's substitute the given values into the equation and calculate v1':

v1' = (5 kg * v1 + 15 kg * 500 m/s - 15 kg * 800 m/s) / 5 kg

Simplifying the equation:

v1' = (5 kg * v1 - 5000 kg*m/s) / 5 kg

v1' = v1 - 1000 m/s

Therefore, the velocity of the smaller fragment after the explosion is equal to its initial velocity minus 1000 m/s.

Now, let's determine the direction of the velocity. Since the larger fragment continues to move in the same direction, we can assume that the smaller fragment also moves in the same direction.

Answer

The velocity of the smaller fragment after the explosion is v1 - 1000 m/s in the same direction as its initial velocity.