On a windless day, the ss sophie germain set out on its maiden voyage. the captain of the ship (captain gauss) told his crew to set their bearings for 25 degrees west of north (n25°w) and the ship set sail at 7 a. m. sharp. the vessel sailed at this heading at a rate of 20 miles per hour, docking at 11: 45 am. gauss and his crew had a leisurely lunch at the cartesian café, who’s slogan "i am…therefore i drink" rang true for the weary travelers. at 2 pm, the sophie germain resumed its seaward journey, heading 12 degrees east of north (n12°e) at a rate of 25 miles per hour until docking safely at 5: 30 pm. the captain and his crew got a room for the night at the nearby newton manor.
1. assuming no wind on the following day, what heading should the germain follow to return directly to its original port?
2. how many miles from the original port, is the ss sophie germain when it sets out on its return voyage?
3. when the germain began its homeward journey the following day, the captain neglected to account for the wind which was blowing 10 miles per hour in the direction of 35 degrees west of north (n35°w). the captain pointed his vessel in the direction of his original port and sailed at 25 miles per hour for one hour and 45 minutes before realizing his mistake.
a. how far from his original port was the ss sophie germain when the captain realized his mistake?
b. assuming the wind remains the same, what direction should the captain point b. his ship now, to head directly to port?