A person walks 37.0◦ north of east for 5.00

km. Another person walks due north and due
east to arrive at the same location.
How large is the east component of this
second path?

use cosine to find the east component. you use the equation x=Vcos37.

5.00km * cos37 will give you the answer.

To find the east component of the second path, we need to use trigonometric concepts.

Let's break down the information given:
- The first person walks 37.0° north of east for 5.00 km.
- The second person walks due north and due east to arrive at the same location.

When the first person walks 37.0° north of east, we can split that motion into two components: one eastward and one northward using trigonometry.

To find the east component of the first person's path:
East Component = distance * cos(angle)

East Component = 5.00 km * cos(37.0°)

Now to determine the second person's path, we know that they walk due north and due east. This implies that they are following a right-angled triangle. From the information given, we can see that the first person's path is the hypotenuse of this triangle.

Using the Pythagorean theorem, we can find the hypotenuse (the first person's path):
Hypotenuse = √(East Component^2 + North Component^2)

We already know the Hypotenuse (5.00 km) and the East Component (found above), so we can rearrange the equation to solve for the North Component.

North Component = √(Hypotenuse^2 - East Component^2)

North Component = √((5.00 km)^2 - (East Component)^2)

Now, we know that the second person walked due east. Since we have determined the East Component, we can conclude that the East Component of the second person's path is the same as the East Component of the first person's path.

Hence, the east component of the second person's path is equal to the east component of the first person's path, which is 5.00 km * cos(37.0°).