Final answer:
To find the athlete's displacement, apply the Pythagorean theorem to the movements north and east, resulting in a displacement of 20 km in a northeast direction.
Step-by-step explanation:
The question asks for the displacement of an athlete who first runs 12 km north and then 16 km east. Displacement is a vector quantity that refers to the change in position of an object and is independent of the path taken by the object.
In this case, the athlete's displacement can be determined by using the Pythagorean theorem since the movement north and east is at right angles to each other.
To find the displacement, we calculate the hypotenuse of a right-angled triangle where the legs are 12 km and 16 km, representing the northward and eastward movements, respectively. Displacement is equal to √(12^2 + 16^2) = √(144 + 256) = √400 km = 20 km. Therefore, the athlete's displacement is 20 km in a northeast direction.