A rocket with initial mass M is launched by emitting, gas wil velocity `v_(0)` (relative to the rocket body) downwards. The mass of the gas emitted per seconds is k. (k is constant and obeys `kv_(0) lt Mg`). Find time when rocket start to lift.

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?

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 of total mass 1000kg initially is launched from ground. The gases are ejected at the rate 20kg/s with velocity 1000 m/s relative to rocket vertically downwards. The initial acceleration of the rocket is a (in m//s^(2) ). Find a/g . (Take g=10 m//s^(2) )

A rocket, with an initial mass of 1000kg , is launched vertically upwards from rest under gravity. The rocket burns fuel at the rate of 10kg per second. The burnt matter is ejected vertically downwards with a speed of 2000ms^-1 relative to the rocket. If burning ceases after one minute, find the maximum velocity of the rocket. (Take g as constant at 10ms^-2 )

A Rocket having initial mass 5xx10^(6)kg , which include mass of fuel of mass 4xx10^(6)kg is ejecting gas with velocity 4000m//s relative to Rocket when entire fuel finishes?

If rocket engine ejects fuel at the rate mu kg/s with relative velocity v_(r) . At time t = 0, speed of rocket is u. Consider the value of acceleration due to gravity is constant and equal to g. Find velocity of rocket as function of time.

A rocket with an initial mass of 1000 kg , is launched vertically upward from rest under gravity. The rocket burns fuel at the rate of 10 kg per second. The burnt matter is ejected vertically downwards with a speed of 2000 m//s relative to the rocket . Find the velocity of the rocket after 1 min of start.

A rocket burns 0.5 kg of fuel per second ejecting it as gases with a velocity of 1600 m//s relative to the rocket . How much force is exerted on the rocket ? Also , calculate the velocity attainted by the rocket , when its mass reduces to (1)/(200) th of its initial mass .

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.

If rocket engine ejects fuel at the rate mu kg/s with relative velocity v_(r) . At time t = 0, speed of rocket is u. Consider the value of acceleration due to gravity is constant and equal to g. If rocket is in gravity free space then find velocity of rocket as function of time.