a girl walks 50m on a bearing 025 and then 200m due east how far is she from the statring point
draw a diagram, and use the law of cosines.
a girl walks 50m on a bearing 025degrees and then 200m due east. how far is she from her starting point
To determine the distance the girl is from the starting point, we can use the concept of vector addition.
First, let's break down the girl's movement into two components:
1. Walking 50 meters on a bearing of 025 degrees: This means the girl is moving 50 meters in a direction 25 degrees clockwise from north.
2. Walking 200 meters due east: This means the girl is moving directly east.
To find the distance from the starting point, we need to consider the horizontal and vertical components of the girl's movement separately.
1. Horizontal Component: The girl walks 200 meters due east, so her displacement in the horizontal direction is 200 meters.
2. Vertical Component: To determine the displacement in the vertical direction, we need to find the vertical component of the distance traveled at a bearing of 025 degrees. Using trigonometry, we can calculate this as follows:
Vertical Component = 50 meters * sin(25°)
Vertical Component ≈ 21.02 meters
Now, we can find the total displacement by combining the horizontal and vertical components:
1. Total Horizontal Displacement (200 meters due east)
2. Total Vertical Displacement (21.02 meters at a bearing of 025 degrees)
To calculate the total displacement, we can use the Pythagorean theorem:
Total Displacement = √(Total Horizontal Displacement^2 + Total Vertical Displacement^2)
Total Displacement = √(200^2 + 21.02^2)
Total Displacement ≈ √(40000 + 441.84)
Total Displacement ≈ √40441.84
Total Displacement ≈ 201.1 meters
Therefore, the girl is approximately 201.1 meters from the starting point.