Use dimensional analysis to derive a possible expression for the drag force \(F_{D}\) on a soccer ball of diameter \(D\) moving at speed \(v\) through air of density \(ho\) and viscosity \(\mu\). [Assuming viscosity has units \(\frac{[M]}{[L][T]}\), there are two possible dimensionless combinations: \(\pi_{1}=\mu D^{\alpha} ho^{\beta} v^{\gamma}\) and \(\pi_{2}=F_{D} D^{\alpha} ho^{\beta} v^{\gamma}\). Determine \(\alpha, \beta\), and \(\gamma\) for each case, and interpret your results.]