Question

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:
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**