$A$ cart is moving with a velocity of $20 \, m/s$. Sand is being dropped into the cart at the rate of $50 \, kg/min$. The force required to move the cart with constant velocity will be ............ $N$.

$A$ rocket of initial mass $6000 \ kg$ ejects gases at a constant rate of $16 \ kg/s$ with a constant relative speed of $11 \ km/s$ in gravity-free space. What is the acceleration of the rocket $1 \ min$ after the blast? (in $m/s^2$)

$A$ 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).

$A$ rocket with a lift-off mass of $3.5 \times 10^4 \ kg$ is blasted upwards with an initial acceleration of $10 \ m/s^2$. The initial thrust of the blast is:

$A$ Diwali rocket of mass $100\,g$ lifts up with an acceleration of $5\,m/s^2$. If gases eject out of the rocket at a rate of $10\,g/s$,then find the velocity of ejection of gas with respect to the rocket in $m/s$.

$A$ rocket with a lift-off mass $2 \times 10^4\,kg$ is blasted upwards with an initial acceleration of $5\,m\,s^{-2}$. The initial thrust of the blast is (Take $g = 10\,m\,s^{-2}$).