A person goes `10 km` north and `20 km` east. What will be displacement from initial point ?

Options

A. `22.36 Km`
B. `2 km`
C. `5 km`
D. `20 km`

Explanation

To find the displacement from the initial point after a person travels 10 km north and 20 km east, we can follow these steps:

### Step 1: Understand the Movement
The person moves 10 km north and then 20 km east. This creates a right triangle where:
- The northward movement (10 km) is one leg of the triangle.
- The eastward movement (20 km) is the other leg of the triangle.

### Step 2: Draw a Diagram
Visualize the movement on a coordinate plane:
- Start at the origin (0,0).
- Move to point A (0,10) after going north.
- Move to point B (20,10) after going east.

### Step 3: Use the Pythagorean Theorem
To find the displacement (the straight-line distance from the starting point to the endpoint), we can use the Pythagorean theorem. The displacement \( S \) can be calculated as follows:

\[ S = \sqrt{(20 \text{ km})^2 + (10 \text{ km})^2} \]

### Step 4: Calculate the Squares
Calculate the squares of the legs of the triangle:
- \( (20 \text{ km})^2 = 400 \text{ km}^2 \)
- \( (10 \text{ km})^2 = 100 \text{ km}^2 \)

### Step 5: Add the Squares
Now, add the squares together:

\[ 400 \text{ km}^2 + 100 \text{ km}^2 = 500 \text{ km}^2 \]

### Step 6: Take the Square Root
Now, take the square root to find the displacement:

\[ S = \sqrt{500 \text{ km}^2} = \sqrt{100 \times 5} = 10 \sqrt{5} \text{ km} \]

### Step 7: Approximate the Value
To find a numerical value for \( \sqrt{5} \), we can use the approximation \( \sqrt{5} \approx 2.236 \):

\[ S \approx 10 \times 2.236 \text{ km} \approx 22.36 \text{ km} \]

### Final Answer
The displacement from the initial point is approximately **22.36 km**.

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