A man travels a distance of 1.5 m towards East, then 2.0 m towards South and finally 4.5 m towards East.
(i) What is the total distance travelled ?
(ii) What is his resultant displacement ?

Options

A. 8 m, 6.3 m
B. 4 m, 6.3 m
C. 12 m, 6.3 m
D. 8m, 12.6 m

Explanation

To solve the problem step by step, we will address both parts of the question: (i) calculating the total distance traveled and (ii) determining the resultant displacement.

### Step-by-step Solution:

**(i) Total Distance Travelled:**
1. **Identify the distances traveled in each direction:**
- First leg: 1.5 m towards East
- Second leg: 2.0 m towards South
- Third leg: 4.5 m towards East

2. **Sum the distances:**
- Total distance = Distance East (1.5 m + 4.5 m) + Distance South (2.0 m)
- Total distance = (1.5 m + 4.5 m) + 2.0 m
- Total distance = 6.0 m + 2.0 m
- Total distance = 8.0 m

**(ii) Resultant Displacement:**
1. **Draw a diagram:**
- Start from the origin (0,0).
- Move 1.5 m East to point A (1.5, 0).
- Move 2.0 m South to point B (1.5, -2.0).
- Move 4.5 m East to point C (6.0, -2.0).

2. **Determine the coordinates:**
- Initial point (origin): O(0, 0)
- Final point: C(6.0, -2.0)

3. **Calculate the displacement:**
- Displacement is the straight-line distance from the initial point O to the final point C.
- Use the distance formula:
\[ \text{Displacement} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]
- Here, \( (x_1, y_1) = (0, 0) \) and \( (x_2, y_2) = (6.0, -2.0) \).
- Substitute the values:
\[ \text{Displacement} = \sqrt{(6.0 - 0)^2 + (-2.0 - 0)^2} \]
\[ = \sqrt{(6.0)^2 + (-2.0)^2} \]
\[ = \sqrt{36 + 4} \]
\[ = \sqrt{40} \]
\[ = 6.32 \, \text{m} \, (\text{approximately}) \]

### Final Answers:
- **Total Distance Travelled:** 8.0 m
- **Resultant Displacement:** 6.32 m (approximately)