A river of width 100 m is flowing with a velocity of 1.5 m/s. A man start from one end with rest relative the river. He raws with an acceleration of `2 m//s^(2)` relative to the river. If the man want to cross the river in minimum time, by how much distance (in meters) will he be drifted (flown) in the direction of river flow during the crossing.

Explanation

To solve the problem of how much distance the man will be drifted downstream while crossing the river, we can break it down into a series of steps:

### Step 1: Understand the Problem
The man is trying to cross a river that is 100 meters wide. The river flows with a velocity of 1.5 m/s. The man starts from rest relative to the river and accelerates at 2 m/s² perpendicular to the river. We need to find out how far downstream he will be drifted while crossing the river in minimum time.

### Step 2: Determine the Time to Cross the River
To find the time taken to cross the river, we use the second equation of motion:
\[ s = ut + \frac{1}{2} a t^2 \]
Where:
- \( s \) is the displacement (100 m, the width of the river),
- \( u \) is the initial velocity (0 m/s, since he starts from rest),
- \( a \) is the acceleration (2 m/s²),
- \( t \) is the time taken.

Plugging in the values:
\[ 100 = 0 \cdot t + \frac{1}{2} \cdot 2 \cdot t^2 \]
This simplifies to:
\[ 100 = t^2 \]
Thus:
\[ t = \sqrt{100} = 10 \text{ seconds} \]

### Step 3: Calculate the Drift
The drift in the direction of the river flow can be calculated using the velocity of the river and the time taken to cross:
\[ \text{Drift} = \text{Velocity of the river} \times \text{Time} \]
Where:
- Velocity of the river = 1.5 m/s,
- Time = 10 seconds.

Calculating the drift:
\[ \text{Drift} = 1.5 \, \text{m/s} \times 10 \, \text{s} = 15 \, \text{meters} \]

### Final Answer
The man will be drifted 15 meters downstream while crossing the river.

---