An engine pumps water continously through a hose. Water leave 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?

Options

A. `(1)/(2) mv^3`
B. `mv^3`
C. `(1)/(2) mv^2`
D. `(1)/(2) m^2 v^3`

Answer

A

Explanation

Rate at which kinetic energy is imparted
`(d K)/(dt) = (d)/(dt) ((1)/(2) M_0 v^2) = (v^2)/(2) (d M_0)/(dt)`
=`(v^2)/(2) (d M_0)/( dl) xx (dl)/(dt) = (v^2)/(2) mv = (1)/(2) m v^3`.