Two trains A and B moving with speed 36 km/hr and 72 km/hr resp. in opposite direction. A Man moving in train A with speed 1.8 km/hr opposite to direction of train. Find velocity of man as seen from train B (in m/s)

Options

A. 32 m/s
B. 29.5 m/s
C. 32.5 m/s
D. 28 m/s

Answer

To find the velocity of the man as seen from train B, we can follow these steps:

### Step 1: Convert the speeds of the trains and the man into meters per second.
- Train A speed: 36 km/hr = \( \frac{36 \times 1000}{3600} = 10 \) m/s
- Train B speed: 72 km/hr = \( \frac{72 \times 1000}{3600} = 20 \) m/s
- Man's speed in train A: 1.8 km/hr = \( \frac{1.8 \times 1000}{3600} = 0.5 \) m/s

### Step 2: Determine the velocity of the man with respect to the ground.
- Since the man is moving opposite to the direction of train A, his velocity with respect to the ground is:
\[ v_{man, ground} = v_{train A} - v_{man} \]
\[ v_{man, ground} = 10 \, \text{m/s} - 0.5 \, \text{m/s} = 9.5 \, \text{m/s} \]

### Step 3: Determine the velocity of the man with respect to train B.
- The velocity of the man with respect to train B is given by:
\[ v_{man, train B} = v_{man, ground} + v_{train B} \]
\[ v_{man, train B} = 9.5 \, \text{m/s} + 20 \, \text{m/s} = 29.5 \, \text{m/s} \]

### Final Answer
The velocity of the man as seen from train B is **29.5 m/s**.

---