A fence post is 52.0 m from where you are standing, in a direction 37.0 degree north of east. A second fence post is due south from you. What is the distance of the second post from you. If the distance between the two posts is 80.0 m?
A fence post is 52.0 m from where you are standing, in a direction 37.0 degree north of east. A second fence post is due south from you. What is the distance of the second post from you. If the distance between the two posts is 80.0 m?
To solve this problem, we can use trigonometry and the concept of vector addition.
Let's break down the given information:
1. We know the distance from where you are standing to the first fence post is 52.0 m. We can call this distance "d1".
2. We also know that the first fence post is located in a direction 37.0 degrees north of east. We can call this angle "θ".
3. The second fence post is due south from where you are standing. Since it is due south, we can consider this direction as 180 degrees.
Now, let's use trigonometry to find the horizontal and vertical components of the first fence post's position:
Horizontal Component (H1): H1 = d1 * cos(θ)
Vertical Component (V1): V1 = d1 * sin(θ)
Using the given values, we can calculate these components:
H1 = 52.0 m * cos(37.0°)
H1 = 52.0 m * 0.7986
H1 ≈ 41.5512 m
V1 = 52.0 m * sin(37.0°)
V1 = 52.0 m * 0.6018
V1 ≈ 31.3156 m
Now, we can find the position of the second fence post relative to your location. Since the second fence post is located due south and the distance between the two posts is given as 80.0 m, the vertical component of the second post's position will be -80.0 m.
Now, we need to find the horizontal component (H2) of the second fence post's position. Since the horizontal component of the first fence post's position (H1) is in the east direction, the horizontal component (H2) of the second fence post's position will be in the west direction.
To find H2, we subtract H1 from the total horizontal distance between the two posts (80.0 m):
H2 = total horizontal distance - H1
H2 = 80.0 m - 41.5512 m
H2 ≈ 38.4488 m
Therefore, the distance of the second fence post from you is given by the Pythagorean theorem:
Distance = sqrt(H2^2 + V2^2)
Distance = sqrt((38.4488 m)^2 + (-80.0 m)^2)
Distance ≈ 89.2226 m
So, the distance of the second fence post from where you are standing is approximately 89.2226 m.