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 $\,N$)

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 ....... $N$.

$A$ rocket is fired upward from the earth's surface such that it creates an acceleration of $19.6 \,m/s^2$. If after $5 \,s$ its engine is switched off,the maximum height of the rocket from the earth's surface would be.........$m$

$A$ 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?

$A$ rocket can go vertically upwards in the Earth's atmosphere because

$A$ rocket is fired vertically up from the ground with a resultant vertical acceleration of $10\ m/s^2$. The fuel is finished in $1\ minute$ and it continues to move up. $(a)$ Find the maximum height reached. $(b)$ After how much time from then will the maximum height be reached? (Take $g = 10\ m/s^2$)