$A$ 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 $50\, s$?

Rocket engines lift a rocket from the earth's surface because hot gas with high velocity

Sand is deposited at a uniform rate of $20 \ kg/s$ and with negligible kinetic energy on an empty conveyor belt moving horizontally at a constant speed of $10 \ m/min$. Find the force required to maintain the constant velocity of the conveyor belt.

$A$ railway wagon of mass $5 \times 10^3 \ kg$ is moving with an initial velocity of $1.2 \ m/s$ on frictionless rails. Rain falls vertically into the wagon. When $10^3 \ kg$ of water has collected in the wagon,what is the change in the kinetic energy of the wagon in $J$?

$A$ 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 $g = 10 \ m \ s^{-2}$)

$A$ 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?