The velocity of water in a river is `2 kmph`,while width is `400 m`. A boat is rowed from a point rowing always aiming opposite point at `8 kmph` of still water velocity. On reaching the opposite bank the drift obtained is

Options

A. `93 m`
B. `100.8 m`
C. `112.4 m`
D. `100 m`

Explanation

To solve the problem of the drift obtained by the boat while crossing the river, we will follow these steps:

### Step 1: Understand the Given Data
- Velocity of water in the river (Vw) = 2 km/h
- Width of the river (d) = 400 m = 0.4 km (since 1 km = 1000 m)
- Velocity of the boat in still water (Vb) = 8 km/h

### Step 2: Calculate the Time Taken to Cross the River
The time (t) taken to cross the river can be calculated using the formula:
\[ t = \frac{d}{Vb} \]
Substituting the values:
\[ t = \frac{0.4 \text{ km}}{8 \text{ km/h}} \]
\[ t = 0.05 \text{ hours} \]

### Step 3: Calculate the Drift
The drift (x) is caused by the velocity of the water acting over the time taken to cross. The formula for drift is:
\[ x = Vw \times t \]
Substituting the values:
\[ x = 2 \text{ km/h} \times 0.05 \text{ hours} \]
\[ x = 0.1 \text{ km} \]

### Step 4: Convert Drift to Meters
To convert the drift from kilometers to meters:
\[ x = 0.1 \text{ km} = 0.1 \times 1000 \text{ m} = 100 \text{ m} \]

### Final Answer
The drift obtained by the boat is **100 meters**.

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