Problem $5(20$ points$)$ You want to study the resultant aerodynamic force on a baseball thrown with spin $($a curveball$).$ This force, $F,$ is assumed to be a function of the ball's speed $V,$ the rotation frequency $f,$ the ball radius $R,$ and the density $$ and viscosity $$ of the fluid.

a$.$ Rewrite this function in terms of the pi groups. Use $V,R,$ and $$ as your repeating variables.

b$.$ In order to study this in a controlled environment, you design a set$-$up to flow air past a spinning ball in a wind tunnel. Your model baseball's radius is $\frac{3}{5}$ of the radius of the real baseball