$A$ cracker rocket is ejecting gases at a rate of $0.05 \,kg/s$ with a velocity of $400 \,m/s$. The accelerating force on the rocket is:

$A$ sand dropper drops sand of mass $m(t)$ on a conveyer belt at a rate proportional to the square root of speed $v$ of the belt,i.e.,$\frac{dm}{dt} \propto \sqrt{v}$. If $P$ is the power delivered to run the belt at constant speed,then which of the following relationships is true?

Sand is being dropped on a conveyor belt at the rate of $2\,kg/s$. The force necessary to keep the belt moving with a constant speed of $3\,m/s$ will be ........... $N$.

$A$ 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?

Can the flight of a rocket be considered projectile motion? Give reasons.

Sand is being dropped on a conveyor belt at the rate of $M \ kg/s$. The force necessary to keep the belt moving with a constant velocity of $v \ m/s$ will be