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Sagot :
Let's solve the problem step-by-step:
1. Calculating Total Distance Traveled:
- First, the ant travels 30 cm eastward.
- Then, it travels 15 cm northward.
- After that, it moves 20 cm westward.
- Finally, it travels 15 cm southward.
To find the total distance traveled, we sum up all these individual distances:
[tex]\[ \text{Total Distance} = 30 \, \text{cm (east)} + 15 \, \text{cm (north)} + 20 \, \text{cm (west)} + 15 \, \text{cm (south)} \][/tex]
This gives us:
[tex]\[ \text{Total Distance} = 30 + 15 + 20 + 15 = 80 \, \text{cm} \][/tex]
2. Calculating Net Displacement:
Displacement is a vector quantity that measures the straight-line distance from the initial to the final position.
- After traveling 30 cm eastward and 20 cm westward, the net movement in the east-west direction is:
[tex]\[ \text{Net East-West} = 30 \, \text{cm} - 20 \, \text{cm} = 10 \, \text{cm east} \][/tex]
- After traveling 15 cm northward and 15 cm southward, the net movement in the north-south direction is:
[tex]\[ \text{Net North-South} = 15 \, \text{cm} - 15 \, \text{cm} = 0 \, \text{cm} \][/tex]
Therefore, the overall net displacement is solely in the eastward direction with no net movement in the north-south direction. So, the displacement vector is 10 cm eastward.
The ant starts and ends up vertically aligned because the northward and southward movements cancel each other out. The overall horizontal movement is 30 cm east minus 20 cm west, resulting in a 10 cm displacement to the east.
Hence, we can summarize the results as follows:
- The Total Distance Traveled is \(80\) cm.
- The Displacement is \(10\) cm.
These results align with our calculations, confirming that:
- The total distance traveled by the ant is \(80\) cm.
- The net straight-line displacement of the ant is [tex]\(10\)[/tex] cm.
1. Calculating Total Distance Traveled:
- First, the ant travels 30 cm eastward.
- Then, it travels 15 cm northward.
- After that, it moves 20 cm westward.
- Finally, it travels 15 cm southward.
To find the total distance traveled, we sum up all these individual distances:
[tex]\[ \text{Total Distance} = 30 \, \text{cm (east)} + 15 \, \text{cm (north)} + 20 \, \text{cm (west)} + 15 \, \text{cm (south)} \][/tex]
This gives us:
[tex]\[ \text{Total Distance} = 30 + 15 + 20 + 15 = 80 \, \text{cm} \][/tex]
2. Calculating Net Displacement:
Displacement is a vector quantity that measures the straight-line distance from the initial to the final position.
- After traveling 30 cm eastward and 20 cm westward, the net movement in the east-west direction is:
[tex]\[ \text{Net East-West} = 30 \, \text{cm} - 20 \, \text{cm} = 10 \, \text{cm east} \][/tex]
- After traveling 15 cm northward and 15 cm southward, the net movement in the north-south direction is:
[tex]\[ \text{Net North-South} = 15 \, \text{cm} - 15 \, \text{cm} = 0 \, \text{cm} \][/tex]
Therefore, the overall net displacement is solely in the eastward direction with no net movement in the north-south direction. So, the displacement vector is 10 cm eastward.
The ant starts and ends up vertically aligned because the northward and southward movements cancel each other out. The overall horizontal movement is 30 cm east minus 20 cm west, resulting in a 10 cm displacement to the east.
Hence, we can summarize the results as follows:
- The Total Distance Traveled is \(80\) cm.
- The Displacement is \(10\) cm.
These results align with our calculations, confirming that:
- The total distance traveled by the ant is \(80\) cm.
- The net straight-line displacement of the ant is [tex]\(10\)[/tex] cm.
Answer:
Calculating Total Distance Traveled:
- First, the ant travels 30 cm eastward.
- Then, it travels 15 cm northward.
- After that, it moves 20 cm westward.
- Finally, it travels 15 cm southward.
To find the total distance traveled, we sum up all these individual distances:
Total Distance
=
30
cm (east)
+
15
cm (north)
+
20
cm (west)
+
15
cm (south)
Total Distance=30cm (east)+15cm (north)+20cm (west)+15cm (south)
This gives us:
Total Distance
=
30
+
15
+
20
+
15
=
80
cm
Total Distance=30+15+20+15=80cm
2. Calculating Net Displacement:
Displacement is a vector quantity that measures the straight-line distance from the initial to the final position.
- After traveling 30 cm eastward and 20 cm westward, the net movement in the east-west direction is:
Net East-West
=
30
cm
−
20
cm
=
10
cm east
Net East-West=30cm−20cm=10cm east
- After traveling 15 cm northward and 15 cm southward, the net movement in the north-south direction is:
Net North-South
=
15
cm
−
15
cm
=
0
cm
Net North-South=15cm−15cm=0cm
Therefore, the overall net displacement is solely in the eastward direction with no net movement in the north-south direction. So, the displacement vector is 10 cm eastward.
The ant starts and ends up vertically aligned because the northward and southward movements cancel each other out. The overall horizontal movement is 30 cm east minus 20 cm west, resulting in a 10 cm displacement to the east.
Hence, we can summarize the results as follows:
- The Total Distance Traveled is \(80\) cm.
- The Displacement is \(10\) cm.
These results align with our calculations, confirming that:
- The total distance traveled by the ant is \(80\) cm.
- The net straight-line displacement of the ant is
10
10 cm.
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