I have a math problem that has me stumped. I cannot seem to find a good starting point for this, and am flying blind with no check values. Maybe it's end of semester fog, but I'm struggling with this. Even another worked-out problem that is similar might help, but I cannot find one in our text.
Beth needs to make a crossing in her canoe from an island to a north-south coastline 3 miles due east. She takes a compass heading 15 degrees north of east and sticks to it all the way across the channel. Tidal currents in the channel push her board southward at a speed proportional to the distance from either shoreline. Beth paddles at 2 miles per hour from west to east.
Beth's eastward speed is: $x'(t)=2\cos(\pi/12)$
Her north-south velocity is: $y'(t)=20.444x(t)(x(t) - 3)+2\cos(\pi/12)$
a) determine a parametrization of Beth's bath across the channel.
b) how far south of her starting point does Beth make landfall?
c) how far does Beth paddle?
d) how long does Beth paddle before she hits landfall?
Thank you!