Question

При взрыве камень разорвался на 3 части. 2 осколка летят под прямым углом друг к другу: m(1осколка)=1к а U(1 осколка)=12 метров/сек; m(2 осколка)=2кг U(2 осколка)=8 метров/сек. 3 кусок отлетает со скоростью 40 метров/сек. Какова m-3 осколка и в каком направлении он летит. Пожалуйста помогите решить и распишите подробно!!! Заранее спасибо!

Answer 1

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Answer 2

Problem Analysis

We have a stone that explodes into three pieces. Two of the fragments fly at right angles to each other, with masses and velocities given. We need to find the mass and direction of the third 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 denote the masses of the three fragments as m1, m2, and m3, and their velocities as v1, v2, and v3, respectively.

The total momentum before the explosion is given by: m1 * v1 + m2 * v2 + m3 * v3 = 0

We are given the masses and velocities of the first two fragments: m1 = 1 kg, v1 = 12 m/s m2 = 2 kg, v2 = 8 m/s

Let's substitute these values into the equation: 1 kg * 12 m/s + 2 kg * 8 m/s + m3 * v3 = 0

Simplifying the equation: 12 kg·m/s + 16 kg·m/s + m3 * v3 = 0 28 kg·m/s + m3 * v3 = 0

Now, we are given the velocity of the third fragment: v3 = 40 m/s

Substituting this value into the equation: 28 kg·m/s + m3 * 40 m/s = 0

Simplifying the equation: 28 kg·m/s + 40 m/s * m3 = 0

To find the mass of the third fragment, we can solve this equation for m3: 40 m/s * m3 = -28 kg·m/s m3 = -28 kg·m/s / 40 m/s m3 = -0.7 kg

The negative sign indicates that the third fragment is moving in the opposite direction to the positive direction we have assumed. Therefore, the mass of the third fragment is 0.7 kg, and it is moving in the opposite direction to the first two fragments.

Answer

The mass of the third fragment is 0.7 kg, and it is moving in the opposite direction to the first two fragments.

Please note that the negative sign indicates the opposite direction.