Starting at the island of Moi in an unknown archipelago, a fishing boat makes a round trip with two stops at the islands of Noi and Poi. It sails from Moi for 4.76 nautical miles (nmi) in a direction 37° north of east to Noi. From Noi, it sails 69° west of north to Poi. On its return leg from Poi, it sails 28° east of south. What distance does the boat sail between Noi and Poi? What distance does it sail between Moi and Poi? Express your answer both in nautical miles and in kilometers. Note: 1 nmi = 1852 m.

A woman sailing a boat is following directions to a dock. First she sails 27.5m 66 degrees NE. Then she travels 35m 22 degrees NW from that position. What is the magnitude and direction of the resultant vector?

You are participating in a summer internship with the Coast Guard. You have been assigned the duty of determining the direction in which a Coast Guard speedboat should travel to intercept unidentified vessels. One day, the radar operator detects an unidentified vessel at a distance of 20.0 km from the radar installation in the direction 15.0° east of north. The vessel is traveling at 26.0 km/h on a course at 40.0° east of north. The Coast Guard wishes to send a speedboat, which travels at 50.0 km/h, to travel in a straight line from the radar installation to intercept and investigate the vessel, and asks you for the heading for the speedboat to take. Express the direction as a compass bearing with respect to due north.

Starting in Albany, you travel a distance 133 miles in a direction 19.6° north of West. Then, from this new position, you travel another distance 491 miles in the direction 42.5° north of East. In your final position, what is your displacement from Albany?

Use your knowledge of bearing, heading, and true course to sketch a diagram that will help you solve the problem.A plane is flying with an airspeed of 140 miles per hour and heading 150°. The wind currents are running at 30 miles per hour at 175° clockwise from due north. Use vectors to find the true course and ground speed of the plane. (Round your answers to the nearest ten for the speed and to the nearest whole number for the angle.)mi/hr with heading °

A plane leaves Denver and travels 239 miles bearing N77 degrees W, then makes a course correction and travels N33 degrees W for 95 miles. How many miles north of Denver did they travel (round to two decimal places)?

An engineer designs a roller coaster so that a car travels horizontally for 192 ft,then climbs 137 ft at an angle of 33.0° above the horizontal. It then moves 137 ft at an angle of 48.0° below the horizontal. If we take the initial horizontal motion of the car to be along the +x-axis, what is the car's displacement? (Give the magnitude of your answer, in ft, to at least four significant figures and give the direction of your answer in degrees counterclockwise from the +x-axis.)

Asha is walking along a straight path from the National Geographic Museum towards the International Spy Museum.  The International Spy Museum is 1.22 km east and 0.91 km south of the National Geographic Museum. Part way along her path, Asha turns perpendicular to the path she was originally following to a second path towards the White House.  The White House is 0.91 km directly south of the National Geographic Museum. Using (0,0) for the location of the National Geographic Museum, determine the slope of the line representing Asha’s second path and write a linear equation for this path.  Show how you arrived at your answer.

A sailboat sets out from the U.S. side of Lake Erie for a point on the Canadian side, 97.0 km due north. The sailor, however, ends up 56.0 km due east of the starting point. (a) How far and (b) in what direction (west of due north) must the sailor now sail to reach the original destination?

On a fine Sunday afternoon, you went malling at the Mall of Asia. Starting from the parking lot, you traveled 240 m in the direction 32 degrees south of east and reached the IMAX theater and watched a movie. After watching a movie, you decided to return back to the parking lot but took different route. From the IMAX theater you traveled a distance X in the direction 48 degrees north of west and a distance Y in the direction 62 degrees south of west and reached the parking lot. What are the magnitudes of distances X and Y?