( 10%) Problem 5: After being deserted by his crew on an island in the Caribbean

Question

( 10%) Problem 5: After being deserted by his crew on an island in the Caribbean, Captain Blackbeard builds a raft to escape and set out to sea on it. The wind seems quite steady, at first blowing him due east for 17 km and then 9 km in a direction 6 degrees north of east Confident that he will eventually reach safety, he falls asleep. When he wakes up, he notices the wind is now blowing him gently 14 degrees south of east, and after traveling for 27 km in that direction, he finds himself back on the island 50% Part (a) How far, as the crow flies, m kilometers, did the wind blow him while he was sleeping? 50% Part b) Assuming the wind blew in the sarne direction all mght, while he was sleeping, what direction in degrees north of west, did the wind blow Jack during the night?

Explanation / Answer

jack

first displacement , r1 = 17 i

second displacement , r2 = 9*cos6i + 9*sin6 j

third displacement r3 = ?

fourth displacement r4 = 27*cos14i - 27*sin14 j

r1 + r2 + r3 + r4 = 0

17i + 9*cos6i + 9*sin6 j + r3 + 27*cos14i - 27*sin14 j = 0

r3 = -52.1 i + 5.6 j

the wind blow a distance of r3 = sqrt(52.1^2+5.59^2) = 52.3 km

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part b

direction = tan^-1(5.6/-52.1) = 6.13 degrees north of west

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