A person walks 23.0° north of east for 2.60 km. How far due north and how far due east would she have to walk to arrive at the same location?
due north- aka find y-component
due east- aka find x-component
http://zonalandeducation.com/mstm/physics/mechanics/vectors/findingComponents/findingComponents.htm
To find the distance due north and due east the person would have to walk to arrive at the same location, we can make use of trigonometry.
Let's break down the information given:
- The person walks 23.0° north of east for 2.60 km.
First, we need to find the component of the displacement in the north direction and the east direction separately.
The component in the north direction can be found using the sine function:
north component (N) = displacement * sin(angle)
N = 2.60 km * sin(23.0°)
Similarly, the component in the east direction can be found using the cosine function:
east component (E) = displacement * cos(angle)
E = 2.60 km * cos(23.0°)
So, to find the distance due north and due east, we can plug in the values into these formulas.
Calculating the north component:
N = 2.60 km * sin(23.0°)
N ≈ 2.60 km * 0.3907
N ≈ 1.0143 km
Calculating the east component:
E = 2.60 km * cos(23.0°)
E ≈ 2.60 km * 0.9205
E ≈ 2.3933 km
Therefore, to arrive at the same location, the person would need to walk approximately 1.0143 km due north and 2.3933 km due east.