Solution:
Let's break down the problem into two parts: the total distance traveled and the displacement.
### Total Distance Traveled
The ant travels in four different segments:
1. Eastward: 30 cm
2. Northward: 15 cm
3. Westward: 20 cm
4. Southward: 15 cm
To find the total distance traveled, we simply add up all the distances of these segments:
[tex]\[ \text{Total Distance} = 30 \text{ cm} + 15 \text{ cm} + 20 \text{ cm} + 15 \text{ cm} \][/tex]
[tex]\[ \text{Total Distance} = 80 \text{ cm} \][/tex]
So, the total distance traveled by the ant is 80 cm.
### Displacement
Displacement is the straight-line distance from the starting point to the ending point. To find this, we need to consider the net movement in the east-west direction and the net movement in the north-south direction.
1. Net East-West Movement:
- The ant moves 30 cm eastward and then 20 cm westward.
- Net East-West Movement = 30 cm (east) - 20 cm (west) = 10 cm eastward.
2. Net North-South Movement:
- The ant moves 15 cm northward and then 15 cm southward.
- Net North-South Movement = 15 cm (north) - 15 cm (south) = 0 cm.
Now, we find the displacement using the Pythagorean theorem. Since the net north-south movement is zero, the displacement is effectively just the net east-west movement.
[tex]\[ \text{Displacement} = \sqrt{(10 \text{ cm})^2 + (0 \text{ cm})^2} \][/tex]
[tex]\[ \text{Displacement} = \sqrt{100} \][/tex]
[tex]\[ \text{Displacement} = 10 \text{ cm} \][/tex]
So, the displacement of the ant is 10 cm.
In conclusion:
- The total distance traveled by the ant is 80 cm.
- The displacement of the ant is 10 cm.
