Clear answers are very helpful At 7AM on a windless thanksgiving, the SS Sopie G

Question

Clear answers are very helpful

At 7AM on a windless thanksgiving, the SS Sopie Germain set out on its maiden voyage. The captain of the ship set his bearings for 25 degrees West of North. The vessel sailed at this heading at a rate of 20 miles per hour, docking at 11:45AM. The captain and his crew had a leisurely lunch at the Cartesian cafe, who's slogan "I drink, therfore I am" rang true for the weary travelers. At 2PM, the Sophie Germain resumed its seaward journey, heading 12 degrees East of North at a rate of 25 miles per hour. The Germain docked safely at 5:30PM. The captain and his crew got a room for the night at 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 25 degrees East of North. The captain pointed his vessel in the direction of his original port and sailed at 15 miles per hour for 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 his ship now, to head directly to port.

4) The captain fixes his heading according to the answer to number (3B) and returns home.

A) How many miles would the Germain have travled from the time it left port on thanksgiving morning to the time it returned home, if the captain had correctly accounted for the wind on the homeward trip?

B) How many extra miles did the Germain travel as a result of the captains error?

5) Draw a model of the situation.

Explanation / Answer

in first stint he travels 95 miles if we take two components : we get 42.3 miles west and 86.1 miles north in 2nd stint he travels 87.5 miles if we take 2 components we get 18.2 miles east and 85.6 miles north add these two we get 14.1 miles west and 171.7 miles north direction to take to get to the port : 4.7 degrees east of south total miles from original port = sqrt(14.1^2 + 171.7^2) = 172.3 miles giving the rest of the answers in comments

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