The city planning commission 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 at right. The equations below represent the riverbanks where x is the number of miles east of City Hall and y is the number of miles north of City Hall. Determine the location for the shortest bridge that will span the Newton River.

North Bank: $y = \cos( \frac { \pi x } { 2 } )+6$ South Bank: $y = \ln(9 - x)$