A model airplane competition has the following rules: Each plane must fly to a point 1 km from the start and then back again. The winner is the plane with the shortest round-trip time. The contestants are free to launch their planes in any direction, so long as the plane travels exactly 1 km out and then returns. On the day of the race, a steady wind blows from the north at 5 m/s. Your plane can maintain an airspeed (speed relative to the air) of 15 m/s, and you know that starting, stopping, and turning times will be negligible. The question: Should you plan to fly into the wind and against the wind on your round-trip, or across the wind flying east and west? Make a reasoned choice by working out the following round-trip times: (1) The plane goes 1 km due north and then back; (2) The plane goes to point 1 km due east of the start, and then back.