Consider a rocket is being fired. The kinetic energy of the rocket is increased by $16$ times, whereas its total mass is reduced by half through the burning of fuel. The factor by which its momentum increases is

$A$ flat plate moves normally with a speed $v_1$ towards a horizontal jet of water of uniform area of cross-section. The jet discharges water at the rate of volume $V$ per second at a speed of $v_2$. The density of water is $\rho$. Assume that water splashes along the surface of the plate at right angles to the original motion. The magnitude of the force acting on the plate due to the jet of water is

$A$ rocket is fired vertically from the ground with a resultant vertical acceleration of $10 \,m/s^2$. The fuel is exhausted in $1 \,min$ and it continues to move up. What is the maximum height reached (in $\,km$)?

$A$ $600\; kg$ rocket is set for a vertical firing. If the exhaust speed is $1000\; m/s$,the mass of the gas ejected per second (in $kg/s$) to supply the thrust needed to overcome the weight of the rocket is

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $20\, m/s^2$. If after $5\, s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be......$m$

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