An engine pumps up $100 \ kg$ of water through a height of $10 \ m$ in $5 \ s$. Given that the efficiency of the engine is $60\%$. If $g = 10 \ m \ s^{-2}$,the power of the engine is .............. $kW$.

Consider a rubber ball freely falling from a height $h = 4.9\, m$ on a horizontal elastic plate. Assume that the duration of collision is negligible and the collision with the plate is totally elastic. Which one of the following graphs represents the velocity as a function of time and the height as a function of time?

$A$ ball of mass $2 \,kg$ is thrown from a tall building with velocity $v = (20 \,m/s) \hat{i} + (24 \,m/s) \hat{j}$ at time $t = 0 \,s$. The change in the potential energy of the ball after $t = 8 \,s$ is (The ball is assumed to be in air during its motion between $0 \,s$ and $8 \,s$, $\hat{i}$ is along the horizontal and $\hat{j}$ is along the vertical direction. Take $g = 10 \,m/s^2$). (in $\,kJ$)

$A$ boat of mass $1000 \,kg$ goes from rest to a speed of $20.0 \,m/s$ in $5.0 \,s$. The water exerts a constant drag force and the acceleration of the boat is constant. If the average power required by the boat is $45000 \,W$, then the magnitude of the drag force is: (in $\,N$)

$A$ truck and a car are moving with equal velocity. On applying the brakes,both will stop after a certain distance. Which of the following is true?

$A$ particle of mass $m$ is dropped from a height $h$ above the ground. At the same time,another particle of the same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2gh}$. If they collide head-on completely inelastically,the time taken for the combined mass to reach the ground,in units of $\sqrt{\frac{h}{g}}$,is