Question

Корпус ракеты массой 200г содержит 300г пороха.Определите скорость выхода газов, если скорость движения ракеты 400м/с. Считайте сгорание пороха мгновенным.

Answer 1

Проекции импульсов на ось ОY имеют разный знак
m1v1-m2v2=0
m1v1=m2v2
v2=m1v1/m2
v2=0,2*400:0,3=267м/с

Answer 2

Calculating Gas Exit Velocity

To calculate the gas exit velocity, we can use the principle of conservation of momentum. The mass of the rocket and the mass of the expelled gas will be involved in the calculation. Given that the rocket's mass is 200g and it contains 300g of gunpowder, and the rocket's velocity is 400m/s, we can calculate the gas exit velocity using the following steps:

1. First, we need to find the velocity of the rocket and the gas relative to the ground. 2. Then, we can use the conservation of momentum to find the gas exit velocity.

Conservation of Momentum

According to the principle of conservation of momentum, the initial momentum of the system (rocket + gas) is equal to the final momentum of the system. The initial momentum is the momentum of the rocket alone, and the final momentum is the momentum of the rocket and the expelled gas.

The initial momentum of the rocket is given by: \[ m_{rocket} \times v_{rocket} \]

The final momentum of the system (rocket + gas) is given by: \[ (m_{rocket} + m_{gas}) \times v_{final} \]

Where: - \( m_{rocket} = 200g = 0.2kg \) (mass of the rocket) - \( m_{gas} = 300g = 0.3kg \) (mass of the expelled gas) - \( v_{rocket} = 400m/s \) (velocity of the rocket) - \( v_{final} \) is the gas exit velocity we want to find

Calculation

Using the conservation of momentum, we can set up the equation: \[ m_{rocket} \times v_{rocket} = (m_{rocket} + m_{gas}) \times v_{final} \]

Solving for \( v_{final} \): \[ v_{final} = \frac{m_{rocket} \times v_{rocket}}{m_{rocket} + m_{gas}} \]

Substituting the given values: \[ v_{final} = \frac{0.2kg \times 400m/s}{0.2kg + 0.3kg} \]

\[ v_{final} = \frac{80}{0.5} \]

\[ v_{final} = 160m/s \]

The gas exit velocity is 160m/s.