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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