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 assertion and reason question regarding the swimmer crossing a river, we will break down the concepts involved step by step.

### Step 1: Understanding the Assertion
The assertion states that to cross the river in minimum time, the swimmer should swim in a direction perpendicular to the water current. This means that if the river flows horizontally (let's say in the x-direction), the swimmer should aim to swim straight across (in the y-direction).

**Hint:** Think about the direction of the swimmer's velocity relative to the river's current.

### Step 2: Analyzing the Reason
The reason given is that the river flow helps to cross the river. However, we need to analyze whether this statement is true. The swimmer's goal is to minimize the time taken to cross the river, and swimming perpendicular to the current does not mean that the current assists in crossing; rather, it affects the swimmer's path.

**Hint:** Consider how the current affects the swimmer's trajectory and whether it aids in crossing directly.

### Step 3: Evaluating the Time Taken to Cross
To determine the time taken to cross the river, we can use the formula for time, which is distance divided by velocity. The distance to cross the river is 'd', and the effective velocity of the swimmer in the y-direction (perpendicular to the current) is 'Vy'. Therefore, the time taken to cross the river is given by:

\[ \text{Time} = \frac{d}{Vy} \]

**Hint:** Remember that the swimmer's speed in the y-direction is crucial for minimizing time.

### Step 4: Understanding the Role of River Flow
The river flow does not help the swimmer cross the river directly; instead, it carries the swimmer downstream while they are swimming across. The swimmer's effective velocity is a combination of their swimming speed and the river's current, but the current does not contribute to the crossing speed.

**Hint:** Think about the vector components of the swimmer's velocity and how they relate to the river's current.

### Step 5: Conclusion
Based on the analysis:
- The assertion is **true**: swimming perpendicular to the current does indeed minimize the time taken to cross the river.
- The reason is **false**: the river flow does not help in crossing; it merely affects the swimmer's path.

Thus, the correct conclusion is that the assertion is true, and the reason is false.

**Final Answer:** Assertion is true, Reason is false.