A river is flowing with a velocity of 2m/s. If the width of river in 100 m and swimmer wants to cross river is shortest time, what time (in sec) would he take if velocity of swimmer in still water is 4 m/s ?

Explanation

To solve the problem of how long it will take the swimmer to cross the river in the shortest time, we can follow these steps:

### Step 1: Understand the Problem
The river flows with a velocity of 2 m/s, and the swimmer has a velocity of 4 m/s in still water. The width of the river is 100 m. The swimmer wants to cross the river in the shortest time possible.

### Step 2: Identify the Components of Velocity
The swimmer's velocity can be broken down into two components:
- The component of the swimmer's velocity that is perpendicular to the river (across the river).
- The component of the swimmer's velocity that is parallel to the river (downstream).

To cross the river in the shortest time, the swimmer should swim directly across the river (perpendicular to the flow), which means he will be affected by the river's current.

### Step 3: Determine the Effective Velocity
The effective velocity of the swimmer across the river (perpendicular to the flow) is his swimming speed, which is 4 m/s. The river's current will carry him downstream while he swims across.

### Step 4: Calculate the Time to Cross the River
The time taken to cross the river can be calculated using the formula:
\[ \text{Time} = \frac{\text{Distance}}{\text{Velocity}} \]
In this case, the distance to cross is the width of the river (100 m) and the velocity across the river is the swimmer's speed (4 m/s).

Substituting the values:
\[ \text{Time} = \frac{100 \text{ m}}{4 \text{ m/s}} = 25 \text{ seconds} \]

### Final Answer
The swimmer will take **25 seconds** to cross the river in the shortest time.

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