# Minimum Power Required

Here is a question, I found two methods to solve it, differing in the answers and I'm not sure why a method is incorrect.

Question: A fire hose of cross section area A is required to direct a jet of water to a height h, the minimum power of the pump needed for this hose is?

Method 1: $$dp = \rho A dxV$$ $$F = \rho A V^2$$ $$P = F.V = \rho A V^3$$

Method 2: $$m = \rho A dx$$ $$KE = \frac{1}{2}mV^2 = \frac{1}{2}\rho A dx V^2$$ $$P = \frac{1}{2}\rho A V^3$$

The correct answer stated is the one obtained from method 2. Can anyone explain why the first method is wrong?