A person walks 11.0° north of east for 3.30 km. How far due north and how far due east would she have to walk to arrive at the same location?
To find the distances due north and due east, we can use trigonometric functions.
Given:
Angle = 11.0° north of east
Distance walked = 3.30 km
To find the distance due north, we can use the sine function:
Distance north = Distance walked * sin(Angle)
Distance north = 3.30 km * sin(11.0°)
Using a calculator, we find:
Distance north = 0.617 km
To find the distance due east, we can use the cosine function:
Distance east = Distance walked * cos(Angle)
Distance east = 3.30 km * cos(11.0°)
Using a calculator, we find:
Distance east = 3.21 km
Therefore, to arrive at the same location, the person would have to walk approximately 0.617 km due north and 3.21 km due east.
To find how far due north and how far due east the person would have to walk to arrive at the same location, we can use trigonometry.
First, let's draw a diagram to represent the situation:
```
11.0° N
/
/ |
/ | 3.30 km
/ |
/ |
/ |
/ |
------------/----------------
X
```
In this diagram, X represents the starting point, and the horizontal line represents the direction due east.
We want to find the distance due north (Y) and the distance due east (X) that the person would have to walk to arrive at the same location.
Using trigonometry, we can break down the original displacement vector (3.30 km at 11.0° north of east) into its north and east components.
The north component can be found using the sine function:
Y = 3.30 km * sin(11.0°)
The east component can be found using the cosine function:
X = 3.30 km * cos(11.0°)
Now, let's calculate Y and X:
Y = 3.30 km * sin(11.0°)
≈ 0.598 km
X = 3.30 km * cos(11.0°)
≈ 3.22 km
Therefore, to arrive at the same location, the person would have to walk approximately 0.598 km due north and 3.22 km due east.