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 three different directions, we can follow these steps:

### Step 1: Understand the movements
The person moves:
- 3 meters to the East
- 4 meters to the North
- 5 meters vertically upwards

### Step 2: Represent the movements in vector form
We can represent these movements using unit vectors:
- East direction can be represented as \(3 \hat{i}\) (where \(\hat{i}\) is the unit vector in the East direction).
- North direction can be represented as \(4 \hat{j}\) (where \(\hat{j}\) is the unit vector in the North direction).
- Upward direction can be represented as \(5 \hat{k}\) (where \(\hat{k}\) is the unit vector in the vertical direction).

Thus, the position vector of the person after all movements can be expressed as:
\[ \vec{r} = 3\hat{i} + 4\hat{j} + 5\hat{k} \]

### Step 3: Calculate the magnitude of the position vector
To find the distance from the starting point, we need to calculate the magnitude of the position vector \(\vec{r}\):
\[ |\vec{r}| = \sqrt{(3)^2 + (4)^2 + (5)^2} \]

### Step 4: Perform the calculations
Calculating the squares:
\[ |\vec{r}| = \sqrt{9 + 16 + 25} \]
\[ |\vec{r}| = \sqrt{50} \]

### Step 5: Simplify the result
We can simplify \(\sqrt{50}\):
\[ |\vec{r}| = \sqrt{25 \times 2} = 5\sqrt{2} \]

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

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