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Section 7.6, # 79

A ship sails first N80 o E for 120 nautical miles and then S20 o W for 200 nautical miles. How far is the ship from it’s starting point, and in what direction. Section 7.6, # 79. To view this file, right click on the file and choose “full screen”. Section 7.6, # 79. North. 120 miles.

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Section 7.6, # 79

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  1. A ship sails first N80oE for 120 nautical miles and then S20oW for 200 nautical miles. How far is the ship from it’s starting point, and in what direction. Section 7.6, # 79 To view this file, right click on the file and choose “full screen”.

  2. Section 7.6, # 79 North 120 miles 80o E u Port 200 miles 20o W Distance to port d v South This distance from the port is the magnitude of vector d.

  3. Find the components of vector u. u = <a,b> 120 miles 80o u 10o a = 120 cos 10o a = 118.2 b = 120 sin 10o b = 20.8 u = <a,b> = < 118.2, 20.8 >

  4. Section 7.6, # 79 North u = < 118.2, 20.8 > 120 miles 80o E u Port 200 miles 20o W Distance to port d v South

  5. Find the components of vector v. 250o c = 200 cos 250o c = -68.4 d = 200 sin 250o d = -187.9 20o 200 miles v v = <c,d> v = <c,d> = < -68.4 , -187.9 >

  6. Section 7.6, # 79 North u = < 118.2, 20.8 > v = < -68.4 , -187.9 > d = u + v d = < 49.8, -167.1 > |d| = |d| = 174.3 miles or 174 miles 120 miles 80o E u Port 200 miles 20o W Distance to port d South v

  7. Find the direction from the port.Answers will vary. d = < 49.8, -167.1 > Find the reference angle tan q = q = tan-1 q = 73.4o -73o 287o d Answers: E73oS or E287oN

  8. Answers will vary. q = 73o Reference angle North Answers: E 73o S or E287oN 270 – 73 = 197 N197oW -73o 287o d

  9. Answers will vary. q = 73o Reference angle Answers: E73oS or E287oN 270 – 73 = 197 N197oW -73o 287o 90 – 73 = 17 S17oE d South

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