A plumber steps down 1 m out of his truck and walks 50m east and then 25m South, and then takes an elevator to the basement of the building 9 m below steet level. If the east, the north and the upwards direction are represent by the positive x, y and z- axes, which one of the following represent displacement (meters ) of the plumber ?

Options

A. `50hati-25hatj-9hatk`
B. `50hati+25hatj-9hatk`
C. `50hati-25hatj-10hatk`
D. `50hati+25hatj-10hatk`

Answer

To find the displacement of the plumber, we need to analyze his movements step by step and represent them in vector form.

### Step-by-Step Solution:

1. **Initial Step Down**:
The plumber steps down 1 meter from his truck. Since the upward direction is positive along the z-axis, stepping down is represented as:
\[ \text{Displacement} = -1 \hat{k} \]

2. **Walking East**:
He walks 50 meters east. The east direction corresponds to the positive x-axis, so this displacement is:
\[ \text{Displacement} = 50 \hat{i} \]

3. **Walking South**:
Next, he walks 25 meters south. The south direction corresponds to the negative y-axis, so this displacement is:
\[ \text{Displacement} = -25 \hat{j} \]

4. **Taking the Elevator Down**:
Finally, he takes an elevator down to the basement, which is 9 meters below street level. This downward movement is also along the z-axis and is represented as:
\[ \text{Displacement} = -9 \hat{k} \]

5. **Total Displacement Calculation**:
Now, we sum all these displacements to find the total displacement vector:
\[ \text{Total Displacement} = (50 \hat{i}) + (-25 \hat{j}) + (-1 \hat{k}) + (-9 \hat{k}) \]
Simplifying this gives:
\[ \text{Total Displacement} = 50 \hat{i} - 25 \hat{j} - 10 \hat{k} \]

Thus, the displacement of the plumber can be represented as:
\[ \text{Displacement} = 50 \hat{i} - 25 \hat{j} - 10 \hat{k} \text{ meters} \]

### Final Answer:
The correct representation of the plumber's displacement is:
\[ \text{Displacement} = 50 \hat{i} - 25 \hat{j} - 10 \hat{k} \text{ meters} \]