Question

Ракета зависла над стартовым столом, выбрасывая вертикально вниз струю газа со скоростью 900 м/с. Найти массу газов, которую должна ежесекундно выбрасывать ракета, чтобы остаться на постоянной высоте, если начальная масса ракеты с топливом равна 10 т.

Answer 1

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Answer 2

To find the mass of gas that the rocket must continuously expel per second in order to remain at a constant height, we can use the principle of conservation of momentum. According to this principle, the change in momentum of the rocket is equal to the momentum of the expelled gas. #### Given information: - Initial mass of the rocket with fuel: 10 tons (10,000 kg) - Gas exhaust velocity: 900 m/s #### Assumptions: - We assume that the rocket is in a vacuum, where there is no air resistance or other external forces acting on it. - We neglect the change in mass of the rocket due to fuel consumption during the time interval considered. #### Solution: Let's denote the mass of gas expelled per second as **dm** and the velocity of the rocket as **v**. According to the principle of conservation of momentum, the change in momentum of the rocket is equal to the momentum of the expelled gas. Mathematically, this can be expressed as: **dm * v = (m + dm) * v' - m * v** Where: - **dm** is the change in mass of the rocket per second (mass of expelled gas) - **v** is the initial velocity of the rocket (900 m/s) - **m** is the initial mass of the rocket (10,000 kg) - **v'** is the final velocity of the rocket (which is assumed to be equal to the initial velocity, as the rocket is at a constant height) Simplifying the equation, we get: **dm * v = dm * v'** Since **v = v'**, the equation becomes: **dm * v = dm * v** This equation tells us that the mass of gas expelled per second (**dm**) must be equal to the initial mass of the rocket (**m**), which is 10,000 kg. Therefore, the rocket must expel a mass of gas equal to 10,000 kg per second in order to remain at a constant height. Please note that this solution assumes ideal conditions and neglects factors such as fuel consumption and the change in mass of the rocket over time. In reality, the mass of the rocket would decrease as fuel is consumed, and the velocity may change due to external forces.