$A$ rocket moves straight upward with zero initial velocity and with an acceleration of $20 \,m/s^2$. It runs out of fuel and stops accelerating at the end of $5^{th} \,sec$. It reaches a maximum height and falls back to the earth. The speed when it hits the ground is (Take $g = 10 \,m/s^2$):

In a rocket, fuel burns at the rate of $1 \,kg / s$. This fuel is ejected from the rocket with a velocity of $60 \,km / s$. The force exerted on the rocket by this is (in $\,N$)

$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. The acceleration of the rocket $50 \ s$ after the blast,neglecting gravity,is $x \ ms^{-2}$. Find the value of $x$.

$A$ solid disc of mass $M$ is held horizontally in the air by throwing $40$ stones per second vertically upwards to strike the disc,each with a velocity of $6\,m/s$. If the mass of each stone is $0.05\,kg$,what is the mass of the disc in $kg$? (Take $g = 10\,m/s^2$)

$A$ rocket accelerates straight up by ejecting gas downwards. In a small time interval $\Delta t$,it ejects a gas of mass $\Delta m$ at a relative speed $u$. Calculate the kinetic energy $(KE)$ of the entire system at time $t + \Delta t$ and $t$,and show that the device that ejects gas does work equal to $(\frac{1}{2}) \Delta m u^2$ in this time interval (ignoring gravity).

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate $\frac{dM}{dt} = \alpha v$,where $M$ is the mass,$v$ is the velocity of the satellite,and $\alpha$ is a constant. What is the deceleration of the satellite?