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 vector addition to find the net displacement of each person.

Let's start with the first person who walks 13.9° north of east for 2.51 km.

Step 1: Find the east and north components of the first person's displacement.
- East Component: 2.51 km * cos(13.9°)
- North Component: 2.51 km * sin(13.9°)

Step 2: Determine the net displacement of the first person.
- Net Displacement: Square root of (east component)^2 + (north component)^2

Now let's move on to the second person who walks due north, then due east.

Step 3: Determine the net displacement of the second person.
- Net Displacement: Square root of (east component)^2 + (north component)^2

Since both persons are at the same location, their net displacements must be equal.

Step 4: Set the net displacement of the first person equal to the net displacement of the second person.

Now we can solve for the distance the second person walks due north and due east.

Let's assume the distance the second person walks due north is represented as "dN" and the distance the second person walks due east is represented as "dE".

For the second person:
- East Component: dE
- North Component: dN

Given that the net displacement of the second person is the same as the net displacement of the first person, we can equate the east and north components:

dE = 2.51 km * cos(13.9°)
dN = 2.51 km * sin(13.9°)

Using these equations, we can calculate the distances the second person walks due north and due east.