Question

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?

• A. $mv^3$
• B. $\frac{1}{2}mv^2$
• C. $\frac{1}{2}m^2v^2$
• D. $\frac{1}{2}mv^3$

Answer 1

Answer: (D)

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

Answer 2

Rate of kinetic energy
But $KE =\frac{d}{d t} \frac{1}{2} M v ^{2}$
But $M =m L$
$KE =\frac{1}{2} \frac{d m}{d t} L v^{2}$
$=\frac{1}{2}\, m v^{3}$