An airline pilot begins a trip to Duluth from an airport located 1500 km (directly) south of Duluth. Her air speed (that is, speed relative to the air) is 260 m/s, but a wind blows from west to east at 40 m/s that takes her off course if she flies directly north (that is, heading north relative to the air). She has the choice of heading slightly westward so that the wind causes her to end up at Duluth or heading due north until she reaches a position directly east of Duluth and then heading west into the wind to Duluth. Find the flight time for each option, and show that heading slightly westward saves about 16 min. You will want to find the plane's ground speed in each case; drawing out the velocity vectors will help.]