Calculus 2 -- Mary needs to make a crossing in her kayak from an island to a north-south coastline 3 miles due east. It is foggy so she cannot see any landmarks to steer by. 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. Mary paddles at 2 miles per hour from west to east. Mary's eastward speed is dx/dt= 2cos(pi/12) and her north-south speed velocity is dy/dt= 20.444x(t)(x(t)-3) + 2cos(pi/12) . Question to follow...

Question

Calculus 2 -- Mary needs to make a crossing in her kayak from an island to a north-south coastline 3 miles due east.  It is foggy so she cannot see any landmarks to steer by.  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.  Mary paddles at 2 miles per hour from west to east.  Mary's eastward speed is dx/dt= 2cos(pi/12) and her north-south speed velocity is dy/dt= 20.444x(t)(x(t)-3) + 2cos(pi/12) .  Question to follow...

anonymous · Answer

Determine a parameterization of Mary's path across the channel. 
How far south of her starting point does Mary make landfall?