A man on a train is walking to the back of a train at a speed of 2m/s while the train is moving forward at 10m/s. Calculate:

Question

1) the man's velocity relative to the train
2) the train's velocity relative to the ground
3) the man's velocity relative to the ground

Answer 1

To solve the problem, let's analyze the motions involved.

1. The man's velocity relative to the train:
   The man is walking backward at 2 m/s while the train is moving forward at 10 m/s. To find the velocity of the man relative to the train, we subtract the speed of the man from the speed of the train: $$\text{Velocity of Man relative to Train}=\text{Velocity of Train}-\text{Velocity of Man}$$ $$=10,\text{m/s}-2,\text{m/s}=8,\text{m/s}$$ So, the man's velocity relative to the train is 8 m/s forward.

2. The train's velocity relative to the ground:
   The train is moving forward at a speed of 10 m/s. Hence, the train's velocity relative to the ground is: $$\text{Velocity of Train relative to Ground}=10,\text{m/s}\text{ (forward)}$$

3. The man's velocity relative to the ground:
   To find the man's velocity relative to the ground, we also need to consider the direction of his walking. Since he is walking backward at 2 m/s while the train, which is seen as forward, is moving at 10 m/s, we get: $$\text{Velocity of Man relative to Ground}=\text{Velocity of Train}-\text{Velocity of Man}$$ $$=10,\text{m/s}-2,\text{m/s}=8,\text{m/s}\text{ (forward)}$$ Thus, the man's velocity relative to the ground is 8 m/s forward.

In summary:

1. The man's velocity relative to the train: 8 m/s forward
2. The train's velocity relative to the ground: 10 m/s forward
3. The man's velocity relative to the ground: 8 m/s forward