Final answer:
The length of the train would be perceived as the same by Anthony (on the train), Miguel (on the platform), and Carolyn (riding a bicycle in the same direction as the train) because they are not dealing with relativistic speeds. All three would agree on the measurement of the train's length.
option e is the correct
Step-by-step explanation:
The question pertains to how the length of a train is perceived by different observers: one on the train, one stationary on the platform, and one moving in the same direction as the train but at a slower speed. This is a classic example involving the principles of special relativity and the perception of simultaneous events.
When dealing with high speeds that are a significant fraction of the speed of light, events that are simultaneous in one frame of reference may not be simultaneous in another due to the finite speed of light and the Lorentz transformation. However, for everyday speeds much less than the speed of light, all observers would agree on the measurement of lengths, such as the length of the train. Thus, assuming that the train and the bicycle are moving at regular, non-relativistic speeds, we can conclude that the train length would be measured the same by all observers, and the correct answer to the question would be that all observers perceive the same train length.
Considering the principles of relative motion, for an observer on the train (Anthony), the train would appear to be stationary relative to him. Therefore, he would perceive the length of the train as its proper length. For an observer on the platform (Miguel), the train is moving, but since we are ignoring relativistic effects, he too would measure the same length as Anthony. For Carolyn, who is moving in the same direction as the train but at a slower speed, the relative speed between her and the train is less than for Miguel, so she too would perceive the train length to be the same. Therefore, the correct order is e. Anthony, Miguel, Carolyn,