$(35$ pts$)$ A sphere is attached by a string to the roof of a wind tunnel in order to provide the tunnel operators with a simple estimate of the wind speed $V$ blowing through the tunnel. Here is some more information:

The diameter of the sphere is $D=2\mathrm{.}13cm$

The specific gravity of the sphere is $SG=0\mathrm{.}855$

Buoyancy forces may be neglected, assuming that the specific gravity was measured in air such that buoyancy has already been taken into account

The air temperature and pressure are $30C$ and $98\mathrm{.}7$ kPa $,$ respectively

The drag on the string is negligible compared to the drag on the sphere

$($a$)$ Construct a free body diagram and then generate an equation for angle $($in degrees$)$ in terms of SG$,{}_{\text{w}\text{a}\text{t}\text{e}\text{r}},{}_{\text{a}\text{i}\text{r}},D,g,V,$ and drag coefficient $C_D.$

$($b$)$ Using the Morrison equation for drag coefficient, calculate angle $($in degrees$)$ when $V=13\mathrm{.}9\frac{m}{s}.$