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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(4) 1/2mv³. Given: the jet leaves at speed v, carrying mass m per unit length. Idea: find how much mass leaves each second, then how much kinetic energy that mass carries. In one second a length v of jet leaves, so the mass leaving per second is (dm)/(dt)=mv. Each kilogram of it carries kinetic energy 1/2v². Rate of kinetic energy =1/2((dm)/(dt))v²=1/2(mv)v². =1/2mv³.

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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