Bearings Question (finding distance travelled)

Question

A ship travel on a bearing of 150^oT for 25km before changing direction to 050^oT and travelling a further 15km. How far south is the ship from it's starting position. (State answer correct to 2 decimal places).

Answer 1

Each of those segments is a vector quantity, with a defined magnitude and direction. To get the final position, we do a "vector addition", meaning that we calculate the net effect of the motions in different directions.

The straightforward way to do this is to first find the vertical and horizontal components, and add them. With bearings, we'll can use the North and East, components which have the same sense as +Y and +X on a conventional graph.

Draw the vectors on graph paper (approximately to scale) and then use the trig formulas to find the components.

For the 2nd leg, the components are:

North: 15 sin 50

East: 15 cos 50