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A man started walking from the supermarket towards his home and walked straight 3 km towards south. Then he turned left and walked 2 km. After that he turned right and walked 3 km. Finally he turned right and walked 5 km. What is the shortest distance between his current position and the supermarket?
- a)10 km
- b)2√5 km
- c)5 km
- d)3√5 km
Correct answer is option 'D'. Can you explain this answer?
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Most Upvoted Answer
A man started walking from the supermarket towards his home and walke...
Given information:
A man starts walking from the supermarket towards his home. He walks in the following sequence:
1. He walks straight 3 km towards the south.
2. He turns left and walks 2 km.
3. He turns right and walks 3 km.
4. Finally, he turns right and walks 5 km.
To find:
The shortest distance between his current position and the supermarket.
Approach:
To find the shortest distance between the man's current position and the supermarket, we need to determine the net displacement of the man. We can use vector addition to calculate the final displacement.
Calculating the displacement:
Let's consider the supermarket as the origin (0, 0) on a coordinate plane. The man's movements can be represented as vectors.
1. The first step is to walk straight 3 km towards the south. This can be represented as a vector (-3, 0) since it has a magnitude of 3 km and is in the negative x-direction.
2. The second step is to turn left and walk 2 km. This can be represented as a vector (0, 2) since it has a magnitude of 2 km and is in the positive y-direction.
3. The third step is to turn right and walk 3 km. This can be represented as a vector (3, 0) since it has a magnitude of 3 km and is in the positive x-direction.
4. The fourth step is to turn right again and walk 5 km. This can be represented as a vector (0, -5) since it has a magnitude of 5 km and is in the negative y-direction.
To calculate the net displacement, we need to add these vectors together:
(-3, 0) + (0, 2) + (3, 0) + (0, -5) = (0, -3)
Calculating the shortest distance:
The net displacement of the man is (0, -3), which means he is 3 km south of the supermarket. To find the shortest distance between his current position and the supermarket, we need to calculate the magnitude of this displacement vector.
Magnitude of the displacement vector = sqrt(0^2 + (-3)^2) = sqrt(0 + 9) = sqrt(9) = 3
Therefore, the shortest distance between his current position and the supermarket is 3 km.
Answer:
The correct answer is option D) 3√5 km.
A man starts walking from the supermarket towards his home. He walks in the following sequence:
1. He walks straight 3 km towards the south.
2. He turns left and walks 2 km.
3. He turns right and walks 3 km.
4. Finally, he turns right and walks 5 km.
To find:
The shortest distance between his current position and the supermarket.
Approach:
To find the shortest distance between the man's current position and the supermarket, we need to determine the net displacement of the man. We can use vector addition to calculate the final displacement.
Calculating the displacement:
Let's consider the supermarket as the origin (0, 0) on a coordinate plane. The man's movements can be represented as vectors.
1. The first step is to walk straight 3 km towards the south. This can be represented as a vector (-3, 0) since it has a magnitude of 3 km and is in the negative x-direction.
2. The second step is to turn left and walk 2 km. This can be represented as a vector (0, 2) since it has a magnitude of 2 km and is in the positive y-direction.
3. The third step is to turn right and walk 3 km. This can be represented as a vector (3, 0) since it has a magnitude of 3 km and is in the positive x-direction.
4. The fourth step is to turn right again and walk 5 km. This can be represented as a vector (0, -5) since it has a magnitude of 5 km and is in the negative y-direction.
To calculate the net displacement, we need to add these vectors together:
(-3, 0) + (0, 2) + (3, 0) + (0, -5) = (0, -3)
Calculating the shortest distance:
The net displacement of the man is (0, -3), which means he is 3 km south of the supermarket. To find the shortest distance between his current position and the supermarket, we need to calculate the magnitude of this displacement vector.
Magnitude of the displacement vector = sqrt(0^2 + (-3)^2) = sqrt(0 + 9) = sqrt(9) = 3
Therefore, the shortest distance between his current position and the supermarket is 3 km.
Answer:
The correct answer is option D) 3√5 km.
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Community Answer
A man started walking from the supermarket towards his home and walke...
Triangle ABC is formed and the shortest distance is AB.
⇒ AB2 = AC2 + BC2 = 62 + 32 = 36 + 9 = 45
⇒ AB = 3√5 km
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A man started walking from the supermarket towards his home and walked straight 3 km towards south. Then he turned left and walked 2 km. After that he turned right and walked 3 km. Finally he turned right and walked 5 km. What is the shortest distance between his current position and the supermarket?a)10 kmb)2√5 kmc)5 kmd)3√5 kmCorrect answer is option 'D'. Can you explain this answer?
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