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You are down at the railyard at 4:30 AM to watch a taping of an Alias episode. You watch as a train goes by at 5.0 m/s south. On top of the train, Agent Sydney Bristow is running north. You see Sydney moving at 8.0 m/s North. At what speed does the camera crew on the train see Sydney running, and in what direction?

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skyluke89

Answer:

The speed is 13 m/s

Explanation:

In this problem, we have two reference frames:

- The reference frame of the observer on the ground, O

- The reference frame of the observes on the train, O', moving with velocity [tex]v' = -5.0 m/s[/tex] with respect to O (here we have taken north as positive direction, so since the train is moving south, we wrote it as a negative number)

For the observer on the ground, O, Sydney is moving with velocity

[tex]v = +8.0 m/s[/tex] (positive because it's moving north)

So, we can find Sydney's velocity with respect to the frame O' as follows

[tex]v=v'+v_s\\v_s = v-v' = +8.0 - (-5.0) = +13 m/s[/tex]

So, the camera crew on the train observe Sydney moving at 13 m/s north

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