Question

Очень надо помогите пожалуйста..:-) ракета масса которой вместе с зарядом равна 250 г взлетает вертикально вверх и достигает высоты 150 м Определить скорость истечения газов из ракеты считая что сгорание заряда происходит мгновенно Масса заряда равна 50 г.

Answer 1

M₁ = 200г - масса ракеты, поднявшейся на высоту.

m₂ = 50г-масса заряда.

Н = 150м - высота подъёма ракеты

g = 9,81 м/с² - ускорение свободного падения

Vр =? - начальная скорость ракеты

Vг=? - скорость газа

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Ракета (уже без заряда) получив импульс m₁·Vр от сгоревшего заряда, равный  m₂·Vг.

Поскольку перед сгоранием заряда ракета с зарядом находились в покое, то эти импулься направлены в противопоожные стороны и равны по величине:

m₂·Vг = m₁·Vр, откуда

Vг = m₁·Vр/m₂.

Остаётся найти начальную скорость ракеты по известной формуле

Vр = √(2gH) = √(2·9,81·150) = √2943 = 54,25 (м/с)

Vг = m₁·Vр/m₂ = 200·54,25/50 = 4·54,25 = 217(м/с)

Ответ: скорость истечения газов 217м/с

Answer 2

Problem Analysis

We are given the mass of a rocket, including its payload, which is 250 g. The rocket launches vertically upwards and reaches a height of 150 m. We need to determine the velocity of the gas exiting the rocket, assuming that the combustion of the payload is instantaneous. The mass of the payload is given as 50 g.

Solution

To solve this problem, we can use the principle of conservation of momentum. According to this principle, the change in momentum of an object is equal to the force applied to it multiplied by the time interval over which the force is applied.

In this case, the force applied to the rocket is the force exerted by the gas exiting the rocket. The change in momentum of the rocket is equal to the momentum of the gas exiting the rocket. We can calculate the momentum of the gas using the equation:

Momentum = mass x velocity

Since the mass of the gas is not given, we can assume that it is equal to the mass of the payload, which is 50 g. Therefore, the momentum of the gas is:

Momentum = 50 g x velocity

The change in momentum of the rocket is equal to the momentum of the gas. We can calculate the change in momentum using the equation:

Change in momentum = mass x change in velocity

The mass of the rocket, including the payload, is given as 250 g. The change in velocity of the rocket is equal to the final velocity of the rocket minus the initial velocity of the rocket. Since the rocket starts from rest, the initial velocity is 0. Therefore, the change in velocity is equal to the final velocity. We can calculate the change in momentum using the equation:

Change in momentum = 250 g x final velocity

Setting the two expressions for the change in momentum equal to each other, we can solve for the final velocity:

50 g x velocity = 250 g x final velocity

Simplifying the equation, we get:

velocity = (250 g / 50 g) x final velocity

Therefore, the velocity of the gas exiting the rocket is equal to five times the final velocity of the rocket.

To find the final velocity of the rocket, we can use the equation for the height reached by an object in free fall:

height = (1/2) x acceleration x time^2

In this case, the acceleration is equal to the acceleration due to gravity, which is approximately 9.8 m/s^2. The time is the time it takes for the rocket to reach the maximum height, which we can calculate using the equation:

time = sqrt(2 x height / acceleration)

Substituting the given values, we can calculate the time:

time = sqrt(2 x 150 m / 9.8 m/s^2)

Once we have the time, we can calculate the final velocity of the rocket using the equation:

final velocity = acceleration x time

Substituting the given values, we can calculate the final velocity:

final velocity = 9.8 m/s^2 x time

Finally, we can calculate the velocity of the gas exiting the rocket by multiplying the final velocity of the rocket by five:

velocity = 5 x final velocity

Let's calculate the final velocity and the velocity of the gas.

Calculation

Using the given values, we can calculate the final velocity and the velocity of the gas as follows:

1. Calculate the time: - height = 150 m - acceleration = 9.8 m/s^2 - time = sqrt(2 x 150 m / 9.8 m/s^2) = 5.43 s

2. Calculate the final velocity of the rocket: - final velocity = 9.8 m/s^2 x 5.43 s = 53.34 m/s

3. Calculate the velocity of the gas: - velocity = 5 x final velocity = 5 x 53.34 m/s = 266.7 m/s

Therefore, the velocity of the gas exiting the rocket is approximately 266.7 m/s.

Conclusion

The velocity of the gas exiting the rocket, assuming instantaneous combustion of the payload, is approximately 266.7 m/s.