In order to leave his island, A man\' builds a raft and sets to sea. The wind fl

Question

In order to leave his island, A man' builds a raft and sets to sea. The wind fluctuates a great deal during the day, and he is blown along the following straight lines: 2.4 km 45.0 degree north of west: then 4.55 km 60.0 degree south of east: then 1.25 km 25.0 degree south of west, then 5.3 km straight east, then 1.7 km 5.00 degree east of north: then 7.45 km 55.0 degree south of west, and finally 2.6 km 10.0 degree north of east. What is the distance of his final position from the island in kilometers? Numeric: A numeric value is expected and not an expression. R= _____ What is the angle of his final position relative to the island? Give your answer in degrees south of east. Numeric: A numeric value is expected and not an expression. a = ______

Explanation / Answer

r1 = 2.4 (-cos45i + sin45) = - 1.70i + 1.70 j

r2 = 4.55 ( cos60i - sin60j) = 2.27i - 3.94j

r3 = 1.25 ( -cos25i - sin25j) = -1.13i - 0.53j

r4 = 5.3i

r5 = 1.7 (sin5i + cos5j) = 0.15i + 1.70j

r6 = 7.45( - cos55i - sin55j) = - 4.27i - 6.10j

r7 = 2.6 (cos10i + sin10j) = 2.56i + 0.45j

r = r1 + r2 +r3 + r4 + r5 + r6 +r7

r = 3.18 i - 6.72 j

(A) distance = sqrt(3.18^2 + 6.72^2)

= 7.43 km

(B) direction = tan^-1(6.72 / 3.18) = 65 deg

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