Question

У ракеті загальна маса якої 200г,є заряд масою 50 г,що згорає миттєво.На яку висоту підніметься ракета,якщо з неї вилітають гази зі швидкістю 600 м/с?Опір повітря у 3 рази зменшує теоретично.

Answer 1

Закон сохранения импульса:
Mv1=mv2
0.2v1=30
v1=150 м/с
Закон сохранения энергии:
mv1^2/2=mgh
h=v1^2/6g( с учетом уменьшения высоты сопротивлением воздуха)
h=375 м

Answer 2

Calculation of Rocket's Height

To calculate the height to which the rocket will rise, we can use the principle of conservation of momentum. The momentum of the rocket before and after the gas is expelled can be equated.

The initial momentum of the rocket is given by the product of its mass and the initial velocity:

Initial momentum = (mass of rocket) * (initial velocity of rocket)

The final momentum of the rocket is given by the product of its mass (after the gas is expelled) and the final velocity (which is zero since the rocket comes to rest at its maximum height):

Final momentum = (mass of rocket - mass of expelled gas) * (final velocity of rocket)

Since momentum is conserved, we can equate the initial and final momenta:

(mass of rocket) * (initial velocity of rocket) = (mass of rocket - mass of expelled gas) * (final velocity of rocket)

We can rearrange this equation to solve for the height to which the rocket will rise:

Height = (mass of expelled gas) * (initial velocity of rocket) / (mass of rocket - mass of expelled gas)

Now let's substitute the given values into the equation and calculate the height.

Given: - Total mass of the rocket (including expelled gas) = 200 g = 0.2 kg - Mass of expelled gas = 50 g = 0.05 kg - Initial velocity of rocket = 600 m/s - Air resistance reduces the theoretical height by a factor of 3

Substituting these values into the equation:

Height = (0.05 kg) * (600 m/s) / (0.2 kg - 0.05 kg)

Simplifying the equation:

Height = (0.05 kg) * (600 m/s) / (0.15 kg)

Height = 20 m/s

Therefore, the rocket will rise to a height of 20 meters.