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 solve the problem, we need to find the velocity of the man moving in train A as observed from train B. Here’s a step-by-step breakdown of the solution:

### Step 1: Convert Speeds from km/hr to m/s
First, we need to convert the speeds of train A, train B, and the man from kilometers per hour (km/hr) to meters per second (m/s).

- Speed of train A = 36 km/hr
\[ \text{Speed of train A in m/s} = 36 \times \frac{5}{18} = 10 \text{ m/s} \]

- Speed of train B = 72 km/hr
\[ \text{Speed of train B in m/s} = 72 \times \frac{5}{18} = 20 \text{ m/s} \]

- Speed of the man = 1.8 km/hr (moving opposite to the direction of train A)
\[ \text{Speed of the man in m/s} = 1.8 \times \frac{5}{18} = 0.5 \text{ m/s} \]

### Step 2: Assign Directions
Since the trains are moving in opposite directions, we can assign directions as follows:
- Let the direction of train A (and the man) be positive.
- Therefore, the velocity of train A = +10 m/s.
- The velocity of train B = -20 m/s (since it is moving in the opposite direction).
- The velocity of the man (moving opposite to train A) = -0.5 m/s.

### Step 3: Calculate Velocity of the Man with Respect to the Ground
To find the velocity of the man with respect to the ground, we can use the formula:
\[ \text{Velocity of man with respect to ground} = \text{Velocity of man with respect to A} + \text{Velocity of A} \]
Substituting the values:
\[ \text{Velocity of man with respect to ground} = -0.5 \text{ m/s} + 10 \text{ m/s} = 9.5 \text{ m/s} \]

### Step 4: Calculate Velocity of the Man with Respect to Train B
Now, we need to find the velocity of the man as seen from train B:
\[ \text{Velocity of man with respect to B} = \text{Velocity of man with respect to ground} - \text{Velocity of B} \]
Substituting the values:
\[ \text{Velocity of man with respect to B} = 9.5 \text{ m/s} - (-20 \text{ m/s}) = 9.5 \text{ m/s} + 20 \text{ m/s} = 29.5 \text{ m/s} \]

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

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