Rate of Kinetic Energy Imparted to Water – Rankers Physics

Power: Practice Problem & Solution

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? (2009)
$mv^3$
$\frac{1}{2}mv^2$
$\frac{1}{2}m^2v^2$
$\frac{1}{2}mv^3$

Solution Explained:

To solve this problem, we apply the core principles of Power. Understanding the underlying formula is key to arriving at the correct answer below:

Mass flowing per second is $\frac{dm}{dt} = mv$. The rate of kinetic energy is $\frac{1}{2} \left(\frac{dm}{dt}\right) v^2 = \frac{1}{2} mv^3$.

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