A traveler first drives 18.8 km east, then 30.3 km southeast, and finally 9.5 km south. Find the traveler's total displacement.

Question

A traveler first drives 18.8 km east, then 30.3 km southeast, and finally 9.5 km south. Find the traveler's total displacement.

magnitude
direction	south of east

Answer 1

Sketch this on graph paper to help visualize.

The straighforward way to add the 3 vectors is to first find the horizontal and vertical components. On a simple x-y plot, we can use +Y for north, -Y for south, +X for east, and -X for west.

2 of the vectors have only one component.

"30.3km southeast resolves to 30.3*sin 45 south (-Y), and 30.3cos 45 east (+X). Add these values to the corresponding value for the other 2 vector.

finally, use the pythagorean theorem to find the magnitude of the sum