Statement-1 : The relative velocity between any two bodies moving in opposite direction is equal to sum of the velocities of two bodies. Statement-2 : Sometimes relative velocity between two bodies is equal to difference in velocities of the two.

Options

A. If both assertion and reason are trure and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not the correct explanations of assertion.
C. If assertion is true but reason is false.
D. If both assertion and reason is false

Explanation

To analyze the statements provided in the question, we can break down the concepts of relative velocity step by step.

### Step 1: Understanding Relative Velocity
Relative velocity is defined as the velocity of one object as observed from another object. It can be calculated using the formula:
\[ V_{AB} = V_A - V_B \]
where \( V_{AB} \) is the relative velocity of object A with respect to object B, \( V_A \) is the velocity of object A, and \( V_B \) is the velocity of object B.

### Step 2: Analyzing Statement 1
Statement 1 claims that the relative velocity between any two bodies moving in opposite directions is equal to the sum of their velocities.
- Let’s assume:
- Body A is moving to the right with velocity \( V_A \).
- Body B is moving to the left with velocity \( V_B \).

In this case, since they are moving in opposite directions, we can express their velocities as:
- \( V_A = V_A \hat{i} \) (to the right)
- \( V_B = -V_B \hat{i} \) (to the left)

Calculating the relative velocity \( V_{AB} \):
\[ V_{AB} = V_A - (-V_B) = V_A + V_B \]
Thus, Statement 1 is correct.

### Step 3: Analyzing Statement 2
Statement 2 states that sometimes the relative velocity between two bodies is equal to the difference in their velocities.
- This is generally true when both bodies are moving in the same direction. For example:
- If Body A is moving to the right with velocity \( V_A \) and Body B is also moving to the right with velocity \( V_B \), then:

Calculating the relative velocity \( V_{AB} \):
\[ V_{AB} = V_A - V_B \]
In this case, the relative velocity is indeed the difference of their velocities. Thus, Statement 2 is also correct.

### Conclusion
Both statements are true:
- Statement 1 is true because when two bodies move in opposite directions, their relative velocity is the sum of their velocities.
- Statement 2 is true because when two bodies move in the same direction, their relative velocity is the difference of their velocities.

### Final Answer
Both assertion and reason are true, and the reason is a correct explanation of the assertion.

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