Lisa is on the west shore of Mighty River, which is 1 mile wide and has two parallel shorelines running exactly north-to-south. She wishes to get to a point on the opposite shore that is 1 mile south of where she is now as quickly as possible. (So this point is $\sqrt2$ miles due southeast from her starting position.) Assuming that Lisa can walk twice as fast as she can swim, and that she wants to swim across the river first before walking any necessary distance along the opposite shoreline, at what course (in degrees) should she start swimming?
(The angle is measured from north, so 90 degrees is due east, meaning she swims directly across the river, and 135 degrees is due southeast, meaning she swims directly to her destination point.)
I know I need to create a function to represent the situation and then find the minimum of the function. I found that $\tan(\theta)$ can be used to find the vertical distance that she travels by swimming ($\theta$ being the angle between the course she swims and the line from her starting point to the point directly across the river). Also, I found that $1 - \tan(\theta)$ is the distance she has to walk after swimming across the river. But I'm not sure how to incorporate the fact that she can walk twice as fast as she can swim. Thanks for the help!
