Thank you for reporting, we will resolve it shortly
Q.
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?
Velocity of water is $v$, mass flowing per unit length is $m$.
$\therefore $ Mass flowing per second $=m v$
$\therefore $ Rate of kinetic energy or K.E. per second
$=\frac{1}{2}(m v) v^{2}=\frac{1}{2} m v^{3} $