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`.

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 rocket is ejecting a mass m of gases per unit time with velocity V relative to the rocket, the thrust on the rocket 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?

Find the law according to which the mass of the rocket varies with time, when the rocket moves with a constant acceleration w, the external forces are absent, the gas escapes with a constant velocity u relative to the rocket, and its mass at the initial moment equals m_0 .

A rocket has a mass of 100 kg . 90% of this is fuel. It ejects fuel vapours at the rate of 1 kg//sec with a velocity of 500 m//sec relative to the rocket. It is supposed that the rocket is outside the gravitational field. The initial upthrust on the rocket when it just starts moving upwards is

A rocket of initial mass m ( including fuel) ejects mass at a constant rate of 25 kg/s with a speed 60 m/s relative to the rocket. If the acceleration of the rocket 3.5 minutes after the firing is 2m//s^(2) . What is the initial mass of the rocket ? [Neglect gravity] Express your answer in unit of 10^(3) kg

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

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.