Answered

QUESTION 2 (Start on a new page.)

An impatient businessman paces up and down while making a business call on his cellphone.

He starts at his desk and walks 5 m east (from A to B) and then walks 7 m west (from B to C). This process takes him 20 s.

2.1 Use a vector scale diagram to represent the two displacements of the man (from A to B and from B to C). Label all the vectors clearly and write down the displacements next to the vectors. Use a scale of 1 cm representing 1 m for your diagram.



Answer :

GinnyAnswer
Alright, let's break down the solution to your question step by step.

### Given Information:
- The businessman walks 5 meters East (from A to B).
- He then walks 7 meters West (from B to C).
- The total time taken for this journey is 20 seconds.

### Questions to Address:
1. Draw a vector scale diagram representing the two displacements.
2. Label all vectors clearly.
3. Write down the displacements next to the vectors using a scale of 1 cm representing 1 m.

### Step-by-Step Solution:

#### 1. Drawing the Vector Scale Diagram:

Since 1 cm on the diagram represents 1 meter, you can use a ruler to be accurate.

From A to B:
- Draw a straight horizontal line towards the right (East direction).
- Label the starting point as A.
- This line should be 5 cm long (because 5 meters scaled down by 1:1 is 5 cm).
- Label the endpoint of this line as B.
- Next to this line, write "5 meters East."

From B to C:
- From point B, draw another straight horizontal line towards the left (West direction).
- This line should be 7 cm long (because 7 meters scaled down by 1:1 is 7 cm).
- Label the endpoint of this line as C.
- Next to this line, write "7 meters West."

Here is a textual representation of the diagram:

```
A -----(5 cm)----> B <-------(7 cm)------ C
| | |
5m East 7m West
```

### Result Details
- The net displacement (total displacement with direction considered), total distance traveled, and average speed:

1. Total Displacement:
- From A to B: 5 meters East.
- From B to C: 7 meters West.
- Since East is considered positive and West negative, the displacement from B to C is -7 meters.
- Therefore, total displacement = [tex]\(5 \, meters + (-7 \, meters) = -2 \, meters\)[/tex].
- The negative sign indicates the final displacement is 2 meters to the West.

2. Average Velocity:
- Total displacement is -2 meters.
- Time taken is 20 seconds.
- Average velocity = [tex]\(\frac{\text{Total Displacement}}{\text{Time Taken}} = \frac{-2 \, \text{meters}}{20 \, \text{seconds}} = -0.1 \, \text{meters/second}\)[/tex].
- The negative sign indicates the direction is West.

3. Total Distance Traveled:
- Distance from A to B is 5 meters.
- Distance from B to C is 7 meters.
- Total distance traveled = [tex]\(5 + 7 = 12 \, \text{meters}\)[/tex].

4. Average Speed:
- Total distance traveled is 12 meters.
- Time taken is 20 seconds.
- Average speed = [tex]\(\frac{\text{Total Distance Travelled}}{\text{Time Taken}} = \frac{12 \, \text{meters}}{20 \, \text{seconds}} = 0.6 \, \text{meters/second}\)[/tex].

So, the final figures are:
- Total Displacement: -2 meters
- Average Velocity: -0.1 meters/second
- Total Distance Traveled: 12 meters
- Average Speed: 0.6 meters/second

Other Questions