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(D) Let the velocity of water be $v$ and the mass per unit length be $m$.The mass of water flowing per unit time (mass flow rate) is given by the prod

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$\frac{1}{2} mv^3$

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(D) Let the velocity of water be $v$ and the mass per unit length be $m$.The mass of water flowing per unit time (mass flow rate) is given by the product of mass per unit length and velocity:$	ext{Mass flow rate} = m 	imes v$The kinetic energy $K$ of a mass $M$ moving with velocity $v$ is $K = \frac{1}{2} Mv^2$.The rate at which kinetic energy is imparted is the power $P$,which is the kinetic energy per unit time:$P = \frac{1}{2} (	ext{mass flow rate}) v^2$$P = \frac{1}{2} (mv) v^2 = \frac{1}{2} mv^3$.

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?

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