White trying to escape his island, Gilligan builds a craft t sets to sea. The wi
ID: 1655401 • Letter: W
Question
White trying to escape his island, Gilligan builds a craft t sets to sea. The wind changes a great deal during the day, t Le is blown along the following straight lines: 2.4 km 45.0 degree north of west: then 4.9 km 60.0 degree south of east, then 1.05 km 25.0 south of west: then 5.4 km straight east, then 1.9 km east of north: then 7.05 km 55.0 degree south of west: and finally 2.85 km 10.0 north of east. a) What is the distance of his final position from the island in kilometers? What is the angle of his final position relative to the island? Give your answer in degrees south of west.Explanation / Answer
r1 = 2.4 (-cos45i + sin45j)
r1 = - 1.70i + 1.70j
r2 = 4.9 (cos60i - sin60j) = 2.45i - 4.24j
r3 = 1.05 (-cos25i - sin25j) = - 0.95i - 0.44j
r4 = 5.4i
r5 = 1.9 (sin45i + cos45j) = 1.34i + 1.34j
r6 = 7.05 (-cos55i - sin55j) = - 4.04i - 5.78j
r7 = 2.85(cos10i + sin10j) = 2.81i + 0.49j
r = r1 +r2 + r3 + r4 + r5 + r6 +r7
r = 5.31i - 6.93j
(A) distance = sqrt(5.31^2 + 6.93^2)
= 8.73 km ......Ans
(B) tan^-1(6.93 / 5.31) = 53 deg south of east
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