A Body moves 6m north, 8m east and 10m vertically upwards, what is its resultant displacement from initial position

Options

A. `10 sqrt(2)m`
B. `10m`
C. `(10)/(sqrt(2))m`
D. `10 xx 2m`

Answer

To find the resultant displacement of a body that moves 6 m north, 8 m east, and 10 m vertically upwards, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Movements**:
- The body moves 6 m north (y-direction).
- The body moves 8 m east (x-direction).
- The body moves 10 m vertically upwards (z-direction).

2. **Represent the Movements in a Coordinate System**:
- Let the initial position of the body be at the origin (0, 0, 0).
- After moving 6 m north, the new position is (0, 6, 0).
- After moving 8 m east, the new position is (8, 6, 0).
- After moving 10 m vertically upwards, the final position is (8, 6, 10).

3. **Calculate the Displacement in the XY Plane**:
- The displacement in the XY plane can be calculated using the Pythagorean theorem.
- The displacement \(d_{xy}\) in the XY plane is given by:
\[ d_{xy} = \sqrt{(x^2 + y^2)} = \sqrt{(8^2 + 6^2)} = \sqrt{(64 + 36)} = \sqrt{100} = 10 \text{ m} \]

4. **Combine the Displacements**:
- Now, we need to find the resultant displacement in 3D space, which includes the vertical displacement (z-direction).
- The resultant displacement \(D\) can be calculated as:
\[ D = \sqrt{(d_{xy}^2 + z^2)} = \sqrt{(10^2 + 10^2)} = \sqrt{(100 + 100)} = \sqrt{200} = 10\sqrt{2} \text{ m} \]

5. **Final Result**:
- The resultant displacement from the initial position is \(10\sqrt{2}\) m.