$3.$ Suppose you buy a $\backslash ($ W $\backslash$times L$=1\mathrm{.}2\backslash$times $4\backslash$mathrm$\{$~m$\}\backslash )$ plywood board and put it on your roof rack as shown on the figure below, the largest dimension aligned along the streamwise direction. You drive home at a speed v $=15$ mph $($better to be careful...$).$

$($a$)$ Assuming the board is perfectly aligned with the airflow, how thick is the boundary layer at the end of the board? $(2$ points$)$

$($b$)$ Estimate the drag on the board of plywood if the boundary layer remains laminar. $(1$ point$)$

$($c$)$ Estimate the drag on the board of plywood if the boundary layer is turbulent $($assume the wood is smooth$)$ and compare the result to that of the laminar boundary layer case. $(1$ point$)$