(2%) Problem 22: In order to escape his island, Gilligan builds a raft and set t
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Question
(2%) Problem 22: In order to escape his island, Gilligan builds a raft and set to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.1 km 45.0° north of west; then 4.75 km 60.0° south of east; then 1 45 km 25.0° south of west; then 5.25 km straight east; then 1.75 km 5.00° east of north; then 7.45 km 55.0° south of west; and finally 2.55 km 10.0 north of east. ?50% Part (a) what is the distance of his final postion from the island in kilometers? south of east. 50% Part (b) what is the angle of his final position relative to the island? Give your answer in degreesExplanation / Answer
A =2.1 ( -cos45i + sin45j )
B=4.75 ( cos60i - sin60j )
C=5.25 i
D=1.45 (-cos 25i- sin25j)
E= 1.75 (cos 85i + sin85j)
F= 7.45 ( - cos 55 i - Sin 55j)
G= 2.55 ( cos 10 i + sin 10j )
R= A+ B + C + D + E+ F + G
R= 3.217 i - 1.9 j
a) net resultant (in magnitude)= (3.217^2+ 1.9^2)^0.5= 3.7365 km.
b) direction
X= arctan( 1.9/3.217)
X= 30.566 South of east.
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