A man walks 4 km towards the north in one hour and then 3 km towards the east in the next hour. His average velocity is

Options

A. `3.5 kmh^(-1)`
B. `2.5 kmh^(-1)`
C. `5 kmh^(-1)`
D. `6 kmh^(-1)`

Answer

To find the average velocity of the man who walks 4 km north and then 3 km east, we can follow these steps:

### Step 1: Understand the Movement
The man first walks 4 km north and then 3 km east. We can visualize this movement on a coordinate system where north is the positive y-direction and east is the positive x-direction.

### Step 2: Calculate the Displacement
Displacement is the straight-line distance from the starting point to the ending point. We can use the Pythagorean theorem to find this distance since the path forms a right triangle.

- The northward distance (vertical leg) = 4 km
- The eastward distance (horizontal leg) = 3 km

Using the Pythagorean theorem:
\[ \text{Displacement} = \sqrt{(4 \text{ km})^2 + (3 \text{ km})^2} \]
\[ = \sqrt{16 + 9} = \sqrt{25} = 5 \text{ km} \]

### Step 3: Calculate the Total Time Taken
The total time taken for the journey is the sum of the time taken for each segment of the walk.

- Time taken to walk 4 km north = 1 hour
- Time taken to walk 3 km east = 1 hour

Total time = 1 hour + 1 hour = 2 hours

### Step 4: Calculate the Average Velocity
Average velocity is defined as the total displacement divided by the total time taken.

\[ \text{Average Velocity} = \frac{\text{Displacement}}{\text{Total Time}} = \frac{5 \text{ km}}{2 \text{ hours}} = 2.5 \text{ km/h} \]

### Final Answer
The average velocity of the man is **2.5 km/h**.

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