Question

)Скорость пули массой 7,9 г при вылете из ствола автомата Калашникова равна 715 м/с . Определите проекцию вектора скорости, сообщаемой автоматчику массой 80 кг, на направление движение пули, если масса автомата равна 3,6 кг.

Answer 1

в этой задаче автоматчик и автомат  - первое тело

m1=80+3.6=83.6

пуля- второе тело

m2=7.9 г =0.0079 кг

v2=715 м/с

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v1  -?

РЕШЕНИЕ

направление скорости пули - положительное

направление скорости автоматчик и автомат -отрицательное

импульс ДО выстрела  p1=0

импульс после австрела p2=p1=0

p2=m1v1 - m2v2 =0  <---------подставим цифры

83.6*v1 -0.0079*715 =0

v1 = 0.0675 м/с = 0.07 м/с

ОТВЕТ 0.0675 м/с = 0.07 м/с

 

Answer 2

Calculation of Projectile Vector

To determine the projection of the velocity vector communicated to the shooter with a mass of 80 kg in the direction of the bullet's motion, we can use the principles of conservation of momentum. The mass of the bullet is 7.9 g, the velocity of the bullet is 715 m/s, and the mass of the rifle is 3.6 kg.

Using the conservation of momentum formula, we can calculate the velocity of the rifle after the bullet is fired. The formula for conservation of momentum is:

Initial momentum = Final momentum

The initial momentum is the momentum of the bullet and the rifle before the bullet is fired, and the final momentum is the momentum of the bullet and the rifle after the bullet is fired.

The initial momentum is the momentum of the rifle, as the bullet is initially at rest. The final momentum is the combined momentum of the bullet and the rifle after the bullet is fired.

Let's calculate the velocity of the rifle after the bullet is fired using the conservation of momentum.

Conservation of Momentum Calculation

The initial momentum of the system (rifle + bullet) is 0, as the bullet is initially at rest. The final momentum of the system is the combined momentum of the bullet and the rifle after the bullet is fired.

The momentum of an object is given by the product of its mass and velocity.

The initial momentum of the rifle is 0, and the final momentum of the system is the sum of the momentum of the bullet and the momentum of the rifle.

The momentum of the bullet is given by: \[ p_{\text{bullet}} = m_{\text{bullet}} \times v_{\text{bullet}} \]

The momentum of the rifle after the bullet is fired is given by: \[ p_{\text{rifle}} = (m_{\text{rifle}} + m_{\text{bullet}}) \times v_{\text{rifle}} \]

Using the conservation of momentum, we can equate the initial and final momenta to solve for the velocity of the rifle after the bullet is fired.

Calculation

The mass of the bullet, \( m_{\text{bullet}} = 7.9 \, \text{g} = 0.0079 \, \text{kg} \)

The velocity of the bullet, \( v_{\text{bullet}} = 715 \, \text{m/s} \)

The mass of the rifle, \( m_{\text{rifle}} = 3.6 \, \text{kg} \)

The mass of the shooter, \( m_{\text{shooter}} = 80 \, \text{kg} \)

The velocity of the rifle after the bullet is fired, \( v_{\text{rifle}} = ? \)

Using the conservation of momentum, we can solve for the velocity of the rifle after the bullet is fired.

\[ p_{\text{bullet}} = p_{\text{rifle}} \] \[ m_{\text{bullet}} \times v_{\text{bullet}} = (m_{\text{rifle}} + m_{\text{shooter}}) \times v_{\text{rifle}} \]

Solving for \( v_{\text{rifle}} \): \[ v_{\text{rifle}} = \frac{m_{\text{bullet}} \times v_{\text{bullet}}}{m_{\text{rifle}} + m_{\text{shooter}}} \]

Substitute the given values to find the velocity of the rifle after the bullet is fired.

\[ v_{\text{rifle}} = \frac{0.0079 \, \text{kg} \times 715 \, \text{m/s}}{3.6 \, \text{kg} + 80 \, \text{kg}} \]

\[ v_{\text{rifle}} \approx 1.11 \, \text{m/s} \]

Conclusion

The projection of the velocity vector communicated to the shooter with a mass of 80 kg on the direction of the bullet's motion is approximately 1.11 m/s.