$A$ 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......$m$

$A$ stationary rocket of initial mass $m_0$ is expelling exhaust gas at a steady speed $v_e$ with respect to itself. There is no external force on the rocket. When its mass is reduced to $\frac{m_0}{2}$,the velocity attained by the rocket will be:

An open carriage in a goods train is moving with a uniform velocity of $10 \,m/s$. If the rain adds water with zero velocity at the rate of $5 \,kg/s$,then the additional force required by the engine to maintain the same velocity of the train is ....... $N$.

$A$ gun of mass $10 \, kg$ fires $4$ bullets per second. The mass of each bullet is $20 \, g$ and the velocity of the bullet when it leaves the gun is $300 \, m/s$. The force required to hold the gun while firing is (in $N$)

$A$ rifle of $20 \,kg$ mass can fire $4$ bullets per second. The mass of each bullet is $35 \times 10^{-3} \,kg$ and its final velocity is $400 \,ms^{-1}$. What force must be applied on the rifle so that it does not move backwards while firing the bullets (in $\,N$)?

$A$ satellite in force-free space sweeps stationary interplanetary dust at a rate of $\frac{d M}{d t} = \alpha v$,where $M$ is the mass,$v$ is the speed of the satellite,and $\alpha$ is a constant. The acceleration of the satellite is: