Question

A ship travels 70 km on a bearing of 27 degrees, and then travels on a bearing of 147 degrees for 180 km. Find the distance of the end of the trip from the starting point.

Answer 1

To find the distance of the end of the trip from the starting point, add the displacements of the two legs of the trip and find the magnitude of the total displacement.

Step-by-step explanation:

To find the distance of the end of the trip from the starting point, we need to add the displacements of the two legs of the trip. Since the ship is on a bearing, we can break each leg into its north and east components.

For the first leg, the north component is 70 km * sin(27°) = 31.9 km and the east component is 70 km * cos(27°) = 61.0 km.

For the second leg, the north component is 180 km * sin(147°) = 152.2 km and the east component is 180 km * cos(147°) = -74.4 km.

Adding the north and east components together, we get a total displacement of 31.9 km + 152.2 km = 184.1 km north and 61.0 km - 74.4 km = -13.4 km east.

The distance of the end of the trip from the starting point is the magnitude of the displacement, which can be found using the Pythagorean theorem: sqrt((184.1 km)^2 + (-13.4 km)^2) = 184.8 km.

Answer 2

70 km 027 degrees ->
north/south 70 * cos(27) = 62.37 (positive so it is to the north)
east/west 70 * sin(27) = 31.779 (positive so it is to the east)

180 kn 147 degrees ->
north/south 180 * cos(147) = -150.961 (negative so it is to the south)
east/west 180 * sin(147) = 98.035 (positive so it is to the east)

sum:
north/south: -88.59
east/west: 129.814

and to find the distance of this point from the starting point:
sqrt(-88.59^2 + 129.814^2)
sqrt(7848.1881 + 16851.768) = 157.16km