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Instantaneous Force and Impulse

An engine pum...

Question

An engine pumps water continuously through a hole. The speed with which water passes through the hole nozzle is v, and k is the mass per unit length of the water jet as it leaves the nozzle. Find the rate at which kinetic energy is being imparted to the water.

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Solution

Considering volume of water flown is $1$ sec,
$K E = \frac{1}{2} {m V}^{2}$
$= \frac{1}{2} (K V) V^{2}$
$= \frac{1}{2} K V^{3}$

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