Question

С какой скоростью будет двигаться судно массой 2000т, плывущее со скоростью 10км/ч, если из закрепленного на нем орудия массой 1000кг вылетает снаряд массой 70кг со скоростью 600м/с против хода судна?

Answer 1

Со скоростью 2,757 м/с или 9,9252 км/ч

Answer 2

Calculating the Speed of the Ship

To calculate the speed of the ship after the projectile is fired, we can use the principle of conservation of momentum. The momentum of an object is the product of its mass and velocity. According to the principle of conservation of momentum, the total momentum before the projectile is fired is equal to the total momentum after the projectile is fired.

The initial momentum of the ship and the projectile is given by: \[ \text{Initial momentum} = \text{Mass} \times \text{Velocity} \]

The final momentum of the ship and the projectile after the projectile is fired is also given by: \[ \text{Final momentum} = \text{Mass} \times \text{Velocity} \]

Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum to solve for the final velocity of the ship.

Calculation

Given: - Mass of the ship, \( m_{\text{ship}} = 2000 \, \text{tons} = 2,000,000 \, \text{kg} \) - Initial velocity of the ship, \( v_{\text{ship}} = 10 \, \text{km/h} = \frac{10}{3.6} \, \text{m/s} \) - Mass of the projectile, \( m_{\text{projectile}} = 70 \, \text{kg} \) - Velocity of the projectile, \( v_{\text{projectile}} = 600 \, \text{m/s} \)

The initial momentum of the ship and the projectile is: \[ \text{Initial momentum} = m_{\text{ship}} \times v_{\text{ship}} \]

The final momentum of the ship and the projectile after the projectile is fired is: \[ \text{Final momentum} = (m_{\text{ship}} + m_{\text{projectile}}) \times v_{\text{final}} \]

Using the principle of conservation of momentum, we can equate the initial momentum to the final momentum: \[ m_{\text{ship}} \times v_{\text{ship}} = (m_{\text{ship}} + m_{\text{projectile}}) \times v_{\text{final}} \]

Solving for \( v_{\text{final}} \), we get: \[ v_{\text{final}} = \frac{m_{\text{ship}} \times v_{\text{ship}}}{m_{\text{ship}} + m_{\text{projectile}}} \]

Substituting the given values, we can calculate the final velocity of the ship.

Calculation Result

\[ v_{\text{final}} = \frac{2,000,000 \times \frac{10}{3.6}}{2,000,000 + 70} \]

\[ v_{\text{final}} \approx 2.7778 \, \text{m/s} \]

So, the final velocity of the ship after the projectile is fired against the direction of the ship's motion is approximately 2.7778 m/s.