A farmer builds three sections of a fence as shown in the figure where L = 10.00 m, and gets tired. Walking straight back to where he started, how far did he go. d=? Vector on Y-axis going to origin, L/2 vector going on Positive X Axis, vector going up L from the end of vector L/2, Vector L slanting from vector L to start of vector d

To determine the total distance the farmer traveled, we need to calculate the lengths of all the vectors involved.

1) The vertical vector going to the origin (Y-axis):
The length of this vector is equal to the height of the fence, which is given as L. Therefore, the length of this vector is L = 10.00 m.

2) The vector going half the distance on the positive X-axis:
The length of this vector is half of L, so it is L/2 = 10.00 m / 2 = 5.00 m.

3) The vertical vector going up from the end of the L/2 vector:
This vector has the same length as the original vertical vector, so its length is also L = 10.00 m.

4) The slanting vector from the end of the L vector to the start of the "d" vector:
This vector's length is also given as L = 10.00 m.

Now, to find the length of the "d" vector, we need to use the Pythagorean theorem:

d² = (L/2)² + L²
d² = (5.00 m)² + (10.00 m)²
d² = 25.00 m² + 100.00 m²
d² = 125.00 m²

Taking the square root of both sides:
d = √(125.00 m²)
d ≈ 11.18 m

Therefore, the farmer went a total distance of approximately 11.18 meters.

To find the distance that the farmer went, we need to add up the lengths of all the vectors.

Let's break it down step by step:

1. Vector 1: The farmer walks a distance of L/2 on the positive X-axis.
- Length of Vector 1 = L/2

2. Vector 2: The farmer walks straight up a distance of L from the end of Vector 1.
- Length of Vector 2 = L

3. Vector 3: The farmer walks a distance of L from the end of Vector 2, slanting towards the starting point.
- Length of Vector 3 = L

4. Vector 4: The farmer walks straight back to where he started, which is along the negative Y-axis.
- Length of Vector 4 = L/2

Now, let's add up the lengths of all the vectors to find the total distance:

Total distance = Length of Vector 1 + Length of Vector 2 + Length of Vector 3 + Length of Vector 4
= L/2 + L + L + L/2

Simplifying the equation further:

Total distance = 2L + 2L/2
= 2L + L
= 3L

Therefore, the total distance that the farmer went is 3 times the length L.

Substituting the given value for L (L = 10.00 m):

Total distance = 3 * 10.00 m
= 30.00 m

So, the farmer went a total distance of 30.00 meters.

d=250

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