A ship is first seen on a radar screen to be 13 km east of the radar site. Some time later, the ship is at 16 km northwest. What is the displacement of the ship from the first location it is seen at?
Displacement = (final vector location) - (initial vector location)
= (-16 sin45 j + 16 cos45 i) - 13 i
= -24.3i + 11.3 j
Which means it moved 24.3 km west and 11.3 km north. "i" and "j" are unit vectors east and north.
The magnitude of the displacement is sqrt[(24.3)^2 + (11.3)^2] = 26.8 km