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

$A$ machine gun is mounted on a $2000 \,kg$ car on a horizontal frictionless surface. At some instant,the gun fires bullets of mass $10 \,g$ with a velocity of $500 \,m/s$ with respect to the car. If the number of bullets fired per second is $10$,the acceleration of the car will be ..... $m/s^2$.

$A$ flexible chain of length $L = 2 \ m$ and mass $M = 1 \ kg$ is initially held in a vertical position such that its lower end just touches a horizontal surface. It is released from rest at time $t = 0$. Assuming that any part of the chain that strikes the plane immediately comes to rest and that the portion of the chain lying on the horizontal surface does not form any heap,find the height of its centre of mass above the surface at the instant $t = 1/\sqrt{5} \ s$ (before it completely comes to rest).

$A$ rocket of mass $5700 \,kg$ ejects mass at a constant rate of $15 \,kg/s$ with a constant speed of $12 \,km/s$. The acceleration of the rocket $1 \,minute$ after the blast is ........... $m/s^2$ $(g=10 \,m/s^2)$.

$A$ balloon with mass $m$ is descending vertically with an acceleration $a$ (where $a < g$). The mass to be removed from the balloon so that it starts moving vertically up with an acceleration $a$ 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?