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