To solve the problem step by step, we will analyze the situation using the principles of conservation of momentum and relative motion.
### Step 1: Understand the Initial Conditions
- The man has a mass of 60 kg and is standing on a boat with a mass of 140 kg.
- Initially, both the man and the boat are at rest, and the man is 20 m away from the shore.
### Step 2: Calculate the Distance the Man Walks
- The man walks towards the shore with a constant speed of 1.5 m/s for a duration of 4 seconds.
- The distance \( S \) that the man covers while walking can be calculated using the formula:
\[
S = \text{speed} \times \text{time} = 1.5 \, \text{m/s} \times 4 \, \text{s} = 6 \, \text{m}
\]
### Step 3: Determine the Movement of the Boat
- As the man walks towards the shore, the boat will move in the opposite direction to conserve the center of mass of the system (man + boat).
- The total mass of the system is \( 60 \, \text{kg} + 140 \, \text{kg} = 200 \, \text{kg} \).
- Using the conservation of momentum:
\[
\text{Initial momentum} = \text{Final momentum}
\]
Initially, the momentum is zero since both are at rest. After the man starts walking:
\[
60 \, \text{kg} \times 1.5 \, \text{m/s} = (60 \, \text{kg} + 140 \, \text{kg}) \times U
\]
Where \( U \) is the speed of the boat in the opposite direction.
### Step 4: Solve for the Speed of the Boat
- The momentum equation becomes:
\[
90 \, \text{kg m/s} = 200 \, \text{kg} \times U
\]
Solving for \( U \):
\[
U = \frac{90}{200} = 0.45 \, \text{m/s}
\]
### Step 5: Calculate the Distance the Boat Moves
- The boat moves for the same duration of 4 seconds:
\[
\text{Distance covered by the boat} = U \times \text{time} = 0.45 \, \text{m/s} \times 4 \, \text{s} = 1.8 \, \text{m}
\]
### Step 6: Calculate the Final Distance from the Shore
- The final distance \( Y \) of the man from the shore can be calculated as:
\[
Y = \text{Initial distance} - \text{Distance covered by the man} + \text{Distance covered by the boat}
\]
Substituting the values:
\[
Y = 20 \, \text{m} - 6 \, \text{m} + 1.8 \, \text{m} = 15.8 \, \text{m}
\]
### Final Answer
The final distance of the man from the shore is **15.8 meters**.
