The city planning board has set aside funds to build a bridge going north and south across the Newton River. To save money, they have agreed to build the shortest bridge possible. A map for the $8$-mile wide city is shown below. The equations below represent the river banks where $x$ is the number of miles east of City Hall and y is the number of miles north of City Hall. Find the location for the shortest bridge that will span the Newton River.

North Bank: $y =\operatorname{cos}( \frac { \pi x } { 2 } )+ 6$

South Bank: $y =\operatorname{ln}(9 − x)$