A train is moving towards East with a speed 20 m/s. A person is running on the roof of the train with a speed 3 m/s against the motion of train. Velocity of the person as seen by an observer on ground will be :

Options

A. 23 m/s towards East
B. 17 m/s towards East
C. 23 m/s towards West
D. 17 m/s towards

Explanation

To solve the problem, we need to find the velocity of a person running on the roof of a train as seen by an observer on the ground. Here's a step-by-step breakdown of the solution:

### Step 1: Identify the velocities
- The train is moving towards the East with a speed of \( V_{train} = 20 \, \text{m/s} \).
- The person is running against the motion of the train (i.e., towards the West) with a speed of \( V_{person} = 3 \, \text{m/s} \).

### Step 2: Determine the direction of velocities
- Since the train is moving East, we can consider East as the positive direction.
- The person running against the train's motion means their velocity is in the negative direction (West).

### Step 3: Calculate the velocity of the person with respect to the ground
- The velocity of the person as seen by an observer on the ground can be calculated using the formula:
\[ V_{relative} = V_{train} - V_{person} \]
- Substituting the values:
\[ V_{relative} = 20 \, \text{m/s} - 3 \, \text{m/s} = 17 \, \text{m/s} \]

### Step 4: Determine the direction of the resultant velocity
- Since the resultant velocity is positive, it indicates that the person is still moving towards the East, even though they are running against the train's motion.

### Final Answer
The velocity of the person as seen by an observer on the ground is \( 17 \, \text{m/s} \) towards the East.

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