two car A and B are moving with velocities of `60 kmh^(-1) and 45 kmh^(-1)` respectively. Calculate the relative velocity of A w.r.t B if (i) both cars are travelling eastwards and (ii)car A is travelling eastwards and car B is travelling westwards.

Options

A. `15 km h^(-1)`
B. `45 km h^(-1)`
C. `60 km h^(-1)`
D. `105 km h^(-1)`

Explanation

To solve the problem of finding the relative velocity of car A with respect to car B under two different scenarios, we can follow these steps:

### Step-by-Step Solution:

**Given:**
- Velocity of car A, \( V_A = 60 \, \text{km/h} \)
- Velocity of car B, \( V_B = 45 \, \text{km/h} \)

**(i) Both cars are traveling eastwards:**

1. **Identify the direction of velocities:**
- Since both cars are moving in the same direction (eastwards), we can simply subtract the velocity of car B from the velocity of car A to find the relative velocity.

2. **Calculate the relative velocity:**
\[ V_{AB} = V_A - V_B = 60 \, \text{km/h} - 45 \, \text{km/h} = 15 \, \text{km/h} \]

3. **Conclusion for the first scenario:**
- The relative velocity of car A with respect to car B when both are traveling eastwards is \( 15 \, \text{km/h} \).

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**(ii) Car A is traveling eastwards and car B is traveling westwards:**

1. **Identify the direction of velocities:**
- Here, car A is moving eastwards, and car B is moving westwards. Since they are moving in opposite directions, we will add their velocities to find the relative velocity.

2. **Calculate the relative velocity:**
\[ V_{AB} = V_A + V_B = 60 \, \text{km/h} + 45 \, \text{km/h} = 105 \, \text{km/h} \]

3. **Conclusion for the second scenario:**
- The relative velocity of car A with respect to car B when car A is traveling eastwards and car B is traveling westwards is \( 105 \, \text{km/h} \).

### Final Answers:
- (i) \( 15 \, \text{km/h} \) (both eastwards)
- (ii) \( 105 \, \text{km/h} \) (A eastwards, B westwards)

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