Assertion: To cross the river in minimum time swimmer should swimming in perpendicular direction to the water current.
Reason: In this case river flow helps to cross this river.

Options

A. If both assertion `&` Reason are True `&` the Reason is a corrrect explanation of the Asserion.
B. If both Assertion `&` Reason are True but Reason is not correct explanation of the Assertion.
C. If Assertion is Trie but the Reason is False.
D. If both Assertion `&` Reason are false

Answer

To solve the question, we need to analyze the assertion and reason provided and determine their validity based on the principles of motion in a plane.

### Step-by-Step Solution:

1. **Understanding the Assertion**:
- The assertion states that to cross the river in minimum time, a swimmer should swim in a direction perpendicular to the water current.
- This implies that the swimmer is aiming to minimize the time taken to cross the width of the river (distance \(d\)).

2. **Analyzing the Motion**:
- When the swimmer swims at an angle \( \theta \) relative to the current, their velocity can be broken down into two components:
- \( v \cos \theta \) (horizontal component, along the direction of the current)
- \( v \sin \theta \) (vertical component, across the river)
- The effective speed of the swimmer in the direction of crossing the river is \( v \sin \theta \).

3. **Time Calculation**:
- The time taken to cross the river can be calculated using the formula:
\[ t = \frac{d}{v \sin \theta} \]
- To minimize the time \( t \), we need to maximize \( v \sin \theta \). The maximum value of \( \sin \theta \) occurs when \( \theta = 90^\circ \), meaning the swimmer swims directly across the river.

4. **Conclusion on the Assertion**:
- Therefore, the assertion is correct: to cross the river in minimum time, the swimmer should swim perpendicular to the current.

5. **Understanding the Reason**:
- The reason states that the river flow helps to cross the river.
- However, the flow of the river only affects the horizontal motion of the swimmer and does not contribute to the vertical motion needed to cross the river. The swimmer must still swim directly across to minimize time.

6. **Conclusion on the Reason**:
- The reason is incorrect because the river flow does not assist in crossing the river; it only affects the swimmer's horizontal displacement.

7. **Final Evaluation**:
- The assertion is true, and the reason is false. Therefore, the correct answer is that the assertion is true, and the reason is false.

### Final Answer:
- Assertion: True
- Reason: False
- Correct Option: C