PLEASE ANSWER BOTH PARTS In order to leave his island, Gilligan builds a raft an

Question

PLEASE ANSWER BOTH PARTS

In order to leave his island, Gilligan builds a raft and sets to sea. The wind shifts a great deal during the day, and he is blown along the following straight lines: 2.05 km 45.0 degree north of west; then 4.65 km 60.0 degree south of east; then 1.05 km 25.0 degree south of west; then 5.5 km straight east; then 1.65 km 5.00 degree east of north; then 7.05 km 55.0 degree south of west; and finally 2.8 km 10.0 degree north of east. What is the distance of his final position from the island in km? What is the angle of his final position relative to the island? Give your answer in degree S of E.

Explanation / Answer

Convert to standard angles,

45º N of W = 135º
60º S of E = 300º

25º S of W = 265º
straight E = 0º

5º E of N =5º

55º S of W = 235º

10º N of E = 10º

Rx= (2.05Cos135 + 4.65Cos300 +1.05Cos265+5.5Cos0+1.65Cos5+7.05Cos235+2.8Cos5)=6.67km

Ry=(2.05sin135 + 4.65sin300 +1.05sin265+5.5sin0+1.65sin5+7.05sin235+2.8sin5)= 9.01 km

In unit vector notation, his final position is 6.67 km i - .9.01 km j,

d = (x² + y²)

= (6.67 ² + -9.01²) = 11.22 km

= arctan(-9.01/6.67) = -53.49º = 53.49º S of East

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