In the jet$-$force lab $($Lab $5),$ you developed the following model to predict the force, $F,$ on a target with an angle $$ with respect to the direction of the impinging jet:

$F=A_j{v}^2(1-cos)$

Force measurements showed that the jet force doubled in going from the $90$ target to the $180$ target.

a$.$ Does the expression cited above explain this observed doubling of the force with the change in the angle? Briefly explain why or why not.

b$.$ Provide a physically$-$based explanation for this observed doubling of the force starting with the momentum balance for a fluid, stated as

$\frac{d}{dt}(M_s{v}_s)=m_1{v}_1-m_2{v}_2-{\displaystyle \underset{i}{\overset{?}{}}}{F}_i$