A man of mass 60 kg is standing on a boat of mass 140 kg, which is at rest in still water. The man is initially at 20 m from the shore. He starts walking on the boat for 4 s with constant speed 1.5 m/s towards the shore. The final distance of the man from the shore is

Options

A. 15.8 m
B. 4.2 m
C. 12.6 m
D. 14.1 m

Answer

To solve the problem step by step, we need to analyze the situation involving the man and the boat.

### Step 1: Understand the Initial Setup
- 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 meters away from the shore.

**Hint:** Identify the masses and the initial distance 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 4 seconds.
- Distance walked by the man = speed × time = 1.5 m/s × 4 s = 6 meters.

**Hint:** Use the formula for distance: Distance = Speed × Time.

### Step 3: Determine the Boat's Movement
- When the man walks towards the shore, the boat will move in the opposite direction due to conservation of momentum.
- The relative displacement of the boat can be calculated using the formula:

\[ \text{Displacement of boat} = \frac{m_{\text{man}} \times d_{\text{man}}}{m_{\text{boat}} + m_{\text{man}}} \]

where:
- \( m_{\text{man}} = 60 \, \text{kg} \)
- \( d_{\text{man}} = 6 \, \text{m} \) (distance walked by the man)
- \( m_{\text{boat}} = 140 \, \text{kg} \)

- Substituting the values:

\[ \text{Displacement of boat} = \frac{60 \, \text{kg} \times 6 \, \text{m}}{140 \, \text{kg} + 60 \, \text{kg}} = \frac{360}{200} = 1.8 \, \text{m} \]

**Hint:** Remember to apply conservation of momentum when one object moves.

### Step 4: Calculate the Final Position of the Man
- The final distance of the man from the shore is given by:

\[ \text{Final distance from shore} = \text{Initial distance from shore} - \text{Distance walked by man} + \text{Displacement of boat} \]

- Substituting the values:

\[ \text{Final distance from shore} = 20 \, \text{m} - 6 \, \text{m} + 1.8 \, \text{m} = 15.8 \, \text{m} \]

**Hint:** Keep track of the directions while calculating the final position.

### Conclusion
The final distance of the man from the shore is **15.8 meters**.

**Final Answer:** 15.8 m (Option 1)