An engine pumps water continuously through a hose. Water leaves the hose with a velocity $v$ and $m$ is the mass per unit length of the water jet. What is the rate at which kinetic energy is imparted to water?

An elevator in a building can carry a maximum of $10$ persons,with the average mass of each person being $68 \; kg$. The mass of the elevator itself is $920 \; kg$ and it moves with a constant speed of $3 \; m/s$. The frictional force opposing the motion is $6000 \; N$. If the elevator is moving up with its full capacity,the power delivered by the motor to the elevator $\left(g = 10 \; m/s^{2}\right)$ must be at least .............. $W$.

$A$ quarter horsepower motor runs at a speed of $600 \ rpm$. Assuming $60 \%$ efficiency,the work done by the motor in one rotation is (in $J$)

Water falls down a $500.0 \,m$ shaft to reach a turbine which generates electricity. How many $m^3$ of water must fall per second in order to generate $1.00 \times 10^9 \,W$ of power? (Assume $50 \%$ efficiency of conversion and $g=10 \,ms^{-2}$)

Why is electrical power required at all when the elevator is descending? Why should there be a limit on the number of passengers in this case?

If the force $\vec{F} = (60\hat{i} + 15\hat{j} - 3\hat{k}) \, N$ and the velocity $\vec{v} = (2\hat{i} - 4\hat{j} + 5\hat{k}) \, m/s$,then what is the instantaneous power in Watts?