$A$ cart loaded with sand is moving with velocity $v$. Sand is falling through a hole as shown in the diagram. After falling on the ground,the sand is:

$A$ rocket which has a 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-

$A$ rocket lifts off from the ground and accelerates upwards at $1 \ m \ s^{-2}$. $20 \ s$ after liftoff, a piece breaks off from the bottom of the rocket. After breaking off, how much time does it take approximately to reach the ground (in $s$)? (Take $g = 10 \ m \ s^{-2}$)

$A$ 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 $N$)

$A$ balloon has a mass of $10\,g$ in air. The air escapes from the balloon at a uniform rate with a velocity of $4.5\,cm/s$. If the balloon shrinks completely in $5\,s$,then the average force acting on the balloon will be (in $dyne$).

The motion of a rocket in an upward direction with high speed is based on the principle of conservation of: