$A$ 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 $50\, s$?

$A$ Diwali rocket of mass $100\,g$ lifts up with an acceleration of $5\,m/s^2$. If gases eject out of the rocket at a rate of $10\,g/s$,then find the velocity of ejection of gas with respect to the rocket in $m/s$.

$A$ rocket is fired vertically up from the ground with a resultant vertical acceleration of $10\ m/s^2$. The fuel is finished in $1\ minute$ and it continues to move up. $(a)$ Find the maximum height reached. $(b)$ After how much time from then will the maximum height be reached? (Take $g = 10\ m/s^2$)

$A$ balloon has $2 \,g$ of air. $A$ small hole is pierced into it. The air comes out with a velocity of $4 \,m/s$. If the balloon shrinks completely in $2.5 \,s$,the average force acting on the balloon is ..........$N$.

$A$ rocket is fired vertically up from the ground with a resultant acceleration of $10\,m/s^2$. The fuel is finished in $1\,min$ and it continues to move up. Take $g=10\,m/s^2$.

$A$ rocket of mass $1000 \, kg$ exhausts gases at a rate of $4 \, kg/s$ with a velocity of $3000 \, m/s$. The thrust developed on the rocket is ........ $N$.