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If a man goes 10 m toward north and 20 m toward east, then his displacement is
- a)22.5 m
- b)32 m
- c)29 m
- d)30 m
Correct answer is option 'A'. Can you explain this answer?
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If a man goes 10 m toward north and 20 m toward east, then his displac...
**Displacement** is the shortest distance between the initial and final positions of an object. It is a vector quantity, meaning it has both magnitude and direction.
In this case, the man moves 10 m toward the north and 20 m toward the east. To find the displacement, we can use the Pythagorean theorem.
**Using the Pythagorean theorem:**
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's consider the displacement as the hypotenuse of a right-angled triangle. The northward movement can be considered as the vertical side, and the eastward movement can be considered as the horizontal side.
**Applying the Pythagorean theorem:**
Using the Pythagorean theorem, we can calculate the displacement as follows:
Displacement = √(vertical^2 + horizontal^2)
Given that the man moves 10 m toward the north and 20 m toward the east, we can substitute these values into the formula:
Displacement = √(10^2 + 20^2)
= √(100 + 400)
= √500
≈ 22.36 m
**Rounding the answer:**
Since the options provided are in whole numbers, we need to round our answer. The closest whole number to 22.36 is 22. Therefore, the correct answer is option 'A' - 22.5 m.
**Explanation:**
The displacement is the straight-line distance between the initial and final positions of an object. In this case, the man moves 10 m toward the north and 20 m toward the east. By using the Pythagorean theorem, we can find the displacement to be approximately 22.36 m. Rounding this value gives us the closest whole number, which is 22. Therefore, the correct answer is option 'A' - 22.5 m.
In this case, the man moves 10 m toward the north and 20 m toward the east. To find the displacement, we can use the Pythagorean theorem.
**Using the Pythagorean theorem:**
The Pythagorean theorem states that in a right-angled triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
Let's consider the displacement as the hypotenuse of a right-angled triangle. The northward movement can be considered as the vertical side, and the eastward movement can be considered as the horizontal side.
**Applying the Pythagorean theorem:**
Using the Pythagorean theorem, we can calculate the displacement as follows:
Displacement = √(vertical^2 + horizontal^2)
Given that the man moves 10 m toward the north and 20 m toward the east, we can substitute these values into the formula:
Displacement = √(10^2 + 20^2)
= √(100 + 400)
= √500
≈ 22.36 m
**Rounding the answer:**
Since the options provided are in whole numbers, we need to round our answer. The closest whole number to 22.36 is 22. Therefore, the correct answer is option 'A' - 22.5 m.
**Explanation:**
The displacement is the straight-line distance between the initial and final positions of an object. In this case, the man moves 10 m toward the north and 20 m toward the east. By using the Pythagorean theorem, we can find the displacement to be approximately 22.36 m. Rounding this value gives us the closest whole number, which is 22. Therefore, the correct answer is option 'A' - 22.5 m.
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