Problem 5: After being left by his crew on an island in the Caribbean, Captain W
ID: 1872336 • Letter: P
Question
Problem 5: After being left by his crew on an island in the Caribbean, Captain William Kidd builds a raft to escape and set out to sea on it. The wind seems quite steady, at first blowing him due east for 1/ km and then 15 km in a direction 8 degrees north °feast. Confident that he will eventually reach safety, he falls asleep when he wakes up, he notices the wind is now blowing him gently 13 degrees south of east, and after traveling for 2 / km in that direction, he finds himself back on the island! Part (a) How far, as the crow flies, in kilometers, did the wind blow him while he was sleeping? Numeric : A numeric value is expected and not an expression. Part (b) Assuming the wind blew in the same direction all night, while he was sleeping, what direction in degrees north of west blow Jack during the night? Numerie : A numeric value is expected and not an expression.Explanation / Answer
a)
Resultant of three vectors
R=[11+15Cos8+21Cos(-13)]i+[15sin8+21Sin(-13)]j
R=46.3 i -2.6 j km
Since he finds where he started
r=-R=-46.3 i +2.6 j km
Magnitude
|r|=sqrt[(-46.3)2+(2.6)2]=46.37 Km
b)
Direction
o=tan-1(2.6/-46.3)=-3.26o