A person walks 13.9◦

north of east for 2.51 km.
Another person walks due north, then due
east to arrive at the same location.
How far due north would this person walk?
How far due east would this person walk?

To solve this problem, we can use trigonometry and vector addition.

Let's break down the movements of both persons:

Person 1:
- Walks 13.9° north of east for 2.51 km.

Person 2:
- Walks due north and due east to reach the same location.

We need to find out how far Person 2 would walk due north and due east.

To solve this, let's consider the displacement of Person 1:

Since Person 1 walks 13.9° north of east, we can split this displacement into its north and east components. To do this, we need to find the east and north components of Person 1's displacement vector.

East component:
The east component is given by the magnitude of the displacement (2.51 km) multiplied by the cosine of the angle (13.9°):
East component = 2.51 km * cos(13.9°)

North component:
The north component is given by the magnitude of the displacement (2.51 km) multiplied by the sine of the angle (13.9°):
North component = 2.51 km * sin(13.9°)

Now, since Person 2 arrives at the same location, their total displacement must be equal to Person 1's displacement. Thus, the north and east components of Person 2's displacement must be equal to Person 1's north and east components, respectively.

Therefore, to find how far Person 2 would walk due north and due east, we just need to use the values we obtained for Person 1:

Distance due north for Person 2 = North component of Person 1
Distance due east for Person 2 = East component of Person 1

Now, let's calculate these distances.

East component of Person 1:
East component = 2.51 km * cos(13.9°)
East component ≈ 2.51 km * 0.9709
East component ≈ 2.439 km

North component of Person 1:
North component = 2.51 km * sin(13.9°)
North component ≈ 2.51 km * 0.2430
North component ≈ 0.610 km

Therefore, Person 2 would walk approximately 0.610 km due north and 2.439 km due east to arrive at the same location.