$A$ rocket of initial mass $1500 \ kg$ ejects gas at a constant rate of $10 \ kg/s$ with a relative speed of $5 \ km/s$. What is the acceleration of the rocket $50 \ s$ after the launch,neglecting gravity (in $m/s^2$)?

$A$ soldier with a machine gun,falling from an airplane,gets detached from his parachute. He is able to resist the downward acceleration if he shoots $40$ bullets per second at a speed of $500 \,m/s$. If the mass of a bullet is $49 \,g$,what is the mass of the man with the gun in $kg$? Ignore air resistance and assume the acceleration due to gravity $g = 9.8 \,m/s^2$.

$A$ 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 ........... $m/s^2$ $(g=10 \,m/s^2)$.

$A$ $2\,kg$ chain is in the form of a heap. Its length is $2\,m$. Its one end is being pulled at a constant speed of $2\,m/s$ horizontally. The power delivered to the chain is (in $W$).

An ice block is melting at a constant rate $\left| \frac{dm}{dt} \right| = \mu$. Its initial mass is $m_0$ and it is moving with velocity $v$ on a frictionless horizontal surface. The distance travelled by it until it melts completely is:

$A$ trolley containing water has a total mass of $4000\, kg$ and is moving at a speed of $40\, m/s$. Water starts leaking from a hole at the bottom of the trolley at a rate of $8\, kg/s$. What is the speed of the trolley after $50\, s$?