A man is standing at point `(x=5m, y=0)` . Then be walks along staight line to `(x=0 , y=5m)` . A second man walks from the same initial position along the x-axis to the arigin and then along the y-axis to `(x=0, y=5m)` . Mark the correct statement(s) :

Options

A. Displacement vector of first man and second man are equal
B. Distance travelled by second man is greater.
C. Magnitude of displacement of second man is same that of first man but direction is different
D. Magnitude of displacement is `sqrt(50)m` for `2^(nd)` man.

Answer

To solve the problem step by step, we will analyze the movements of both men and determine the correct statements based on their displacements and distances traveled.

### Step 1: Identify the Positions
- The first man starts at point \( P(5, 0) \) and walks to point \( Q(0, 5) \).
- The second man also starts at point \( P(5, 0) \), walks to the origin \( O(0, 0) \), and then to point \( Q(0, 5) \).

### Step 2: Calculate the Displacement of Both Men
- **Displacement of the First Man (A)**:
- The displacement vector from \( P \) to \( Q \) can be calculated as:
\[ \text{Displacement (A)} = Q - P = (0, 5) - (5, 0) = (-5, 5) \]

- **Displacement of the Second Man (B)**:
- The displacement vector from \( P \) to \( Q \) is the same:
\[ \text{Displacement (B)} = Q - P = (0, 5) - (5, 0) = (-5, 5) \]

### Step 3: Compare the Displacements
- Both men have the same displacement vector \( (-5, 5) \). Thus, the magnitude and direction of their displacements are equal.

### Step 4: Calculate the Distance Traveled by Both Men
- **Distance Traveled by the First Man (A)**:
- The distance traveled is simply the length of the straight line from \( P \) to \( Q \):
\[ \text{Distance (A)} = \sqrt{(0 - 5)^2 + (5 - 0)^2} = \sqrt{25 + 25} = \sqrt{50} \text{ m} \]

- **Distance Traveled by the Second Man (B)**:
- The second man travels from \( P \) to \( O \) and then to \( Q \):
\[ \text{Distance (B)} = OP + OQ = 5 \text{ m} + 5 \text{ m} = 10 \text{ m} \]

### Step 5: Analyze the Statements
1. **Statement A**: The displacement vector for the first man and second man are equal.
- **True**: Both have the same displacement vector \( (-5, 5) \).

2. **Statement B**: The distance traveled by the second man is greater.
- **True**: Distance traveled by man A is \( \sqrt{50} \) m, while man B travels \( 10 \) m.

3. **Statement C**: The magnitude of displacement of the second man is the same as that of the first man, but the direction is different.
- **False**: Both the magnitude and direction of displacement are the same for both men.

4. **Statement D**: The magnitude of displacement is \( \sqrt{50} \) m for the second man.
- **False**: The magnitude of displacement for both men is \( \sqrt{50} \) m, not just for the second man.

### Conclusion
The correct statements are:
- Statement A: True
- Statement B: True
- Statement C: False
- Statement D: False

### Final Answer
The correct options are A and B.