Past exam of the mathematics course of the University of Cambridge / 2007 / ib / Paper 1 / 17D / iii / Solution

At the cone's vertex height $h$, the first part gives $U(h)=U_0\sqrt{1-2gh/U_0^2}$ and $A(h)U(h)=A_0{U}_0$. Insert these into the assumed local impingement force from part (ii). Static support requires upward force equal to $Mg$, givingEquivalently,For a nonnegative support height the ratio in parentheses must not exceed one, and the prescribed $h\ll U_0^2/(2g)$ requires that ratio to be close to one. If the weight exceeds the lift available at the nozzle, this model has no supported height above the nozzle.