1. The problem statement, all variables and given/known data B7 State the relationships between (i) force and momentum, (ii) force and energy, (iii) force and power, (iv) power and energy.  Find expressions for the momentum and kinetic energy transported per unit time in a jet of ﬂuid having cross-sectional area A, density ρ, and speed u. In a water pistol, a trigger drives a piston at constant speed along a cylinder with cross-sectional area S forcing water out through a hole as a narrow jet with cross-sectional area A. By equating the power supplied to the piston to that transported by the jet show that the net force F needed on the piston to generate a jet with speed u is F = 1/2 x pSu^2 where ρ is the density of water.  A pistol has S = 1cm2 and A = 4mm2. A target is placed at a height h = 2.5m above the pistol and at a distance w = 5m in front of it. Find the speed of the jet needed, the direction in which the pistol must be aimed, and the force needed on the piston, to produce a jet that hits the target horizontally.  Is the force of the jet suﬃcient to dislodge a target with a mass of 30g on a surface with a coeﬃcient of friction of 0.5?  [ You may assume that the density of water is ρ = 1,000kgm−3 ] 2. Relevant equations 3. The attempt at a solution Ok for the first four questions I put : i) Force x time = momentum ii) Force x distance = Energy iii) (Force x distance)/time = Power iv) Energy/time = Power For the next part I used the logic that momentum per unit time would have units kgms^(-2) and by using area= m^2 , density= kgm^(-3) and speed = ms^(-1) I arrived at the correct units using density x speed^2 x area = pAu^2 I used a similar method for kinetic energy per unit time time and arrived at ke per time = 1/2 x pAu^3 I'm not sure if these are correct. For the next part I started with the power transported by the jet = KE/time = 1/2pAu^3 But then I don't know how to find the power supplied to the piston, I know that using the equation from iii) I can get something in terms of F but I don't know the time or distance nor how I get S involved. Help would be much appreciated!