A rocket ejects a steady jet whose velocity is equal to u relative to the rocket. The gas discharge rate equals `mu kg//s`. Demonstrate that the rocket motion equation in this case takes the form
`mw=F-muu`,
where m is the mass of the rocket at a given moment, w is its acceleration, and F is the external force.

A rocket moves in the absence of external forces by ejecting a steady jet with velocity u constant relative to the rocket. Find the velocity v of the rocket at the moment when its mass is equal to m, if at the initial moment it possessed the mass m_0 and its velocity was equal to zero. Make use of the formula given in the foregoing problem.

A relativistic rocket emits a gas jet with non-relativistic velocity u constant relative to the rocket. Find how the velocity v of the rocket depends on its rest mass m if the initial rest mass of the rocket equals to m_0 .

The rate of mass of the gas emitted from the rear of a rocket is initially 0.1 kg//s . If the speed of the gas relative to the rocket is 50 m//s and the mass of the rocket is 2 kg , then the acceleration of the rocket in m//s^(2) is

A double stage rocket has an initial mass M_(i) , gas is exhausted front he rocket at a constant rate of dm/dt and with an exhaust velocity u relative to the rocket. When the mass of the rocket reaches the value mu , the first stage of mass m of Which fuel is exhausted is disengaged from the rocket and then the rocket continues to the second stage at teh same rate and exhaust velocity as int eh first stage, until it reaches a mass M_(f) (a). Calculate the rocket velocity at the end of the first stage, given that it is started at rest. (b). Calculat ethe rocket velocity at the end of the second stage. ltbr. (c). What is the final velocity of a one stage rocket of the same initial M_(i) mass and the same amount of fuel ? it is greater or less than final velocity of the double stage rocket?

If M is mass of rocket, r is rate of ejection of gases and u is velocity of gases with respect to rocket then acceleration of the rocket dv/dt is equal to

In a rocket, fuel bums at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to

In a rocket, fuel bums at the rate of 1 kg/s. This fuel is ejected from the rocket with a velocity of 60 km/s. This exerts a force on the rocket equal to

During the rocket propulsion, gases ejecting with velocity 1 km/s relative to rocket. The rate of fuel consumption is (m)/(10) kg/s, where m is the instantaneous mass of the rocket. If air ressitance varies according to equation f = 0.15 mv, then terminal velocity of the rocket is -