Julia can swim at 3.5 km/hr in still water. she attempts to head straight north across a river with a current
flowing at 1.2 km/hr [w]. what is her resultant velocity?

-- Relative to the water, Julia's velocity is  3.5 km/hr to the north.

-- Relative to the shore, her velocity is

                 (3.5 km/hr north) + (1.2 km/hr west)

             =  √ (3.5² + 1.2²)   arctan(3.5/1.2) north of west

             =  √13.69              arctan(2.91666...) north of west

             =    3.7 km/hr  towards  71° north of west .