A person moves towards East for 3 m, then towards North for 4 m and then moves vertically up by 5 m. What is his distance now from the starting point ?

Options

A. `5sqrt(2)m`
B. 5 m
C. 10 m
D. 20 m

Explanation

To find the distance of the person from the starting point after moving in the specified directions, we can follow these steps:

### Step 1: Define the starting point
Let's assume the starting point of the person is at the origin of a coordinate system, which can be represented as (0, 0, 0).

### Step 2: Determine the coordinates after each movement
1. **First Movement**: The person moves 3 meters towards the East. In our coordinate system, this corresponds to the positive x-direction. The new coordinates will be:
\[ (3, 0, 0) \]

2. **Second Movement**: The person then moves 4 meters towards the North. This corresponds to the positive y-direction. The new coordinates will be:
\[ (3, 4, 0) \]

3. **Third Movement**: Finally, the person moves vertically up by 5 meters, which corresponds to the positive z-direction. The final coordinates will be:
\[ (3, 4, 5) \]

### Step 3: Calculate the distance from the starting point
To find the distance from the starting point (0, 0, 0) to the final point (3, 4, 5), we can use the distance formula in three dimensions:
\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2 + (z_2 - z_1)^2} \]
Substituting the coordinates:
\[ d = \sqrt{(3 - 0)^2 + (4 - 0)^2 + (5 - 0)^2} \]
\[ d = \sqrt{3^2 + 4^2 + 5^2} \]
\[ d = \sqrt{9 + 16 + 25} \]
\[ d = \sqrt{50} \]
\[ d = 5\sqrt{2} \]

### Conclusion
The distance of the person from the starting point is \(5\sqrt{2}\) meters.

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