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what if? suppose one of the professors proctored the exam by traveling on spacecraft i and stopped the exam after 88.0 min elapsed on her clock. (c) for what time interval (in minutes) does the exam last as measured by the professors on spacecraft ii?

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According to the theory of relativity, time appears to pass more slowly for an object that is moving relative to an observer. This effect, known as time dilation, becomes significant at high speeds close to the speed of light.

In this scenario, the professor on spacecraft I is moving relative to the professor on spacecraft II. As a result, time will appear to pass more slowly for the professor on spacecraft I compared to the professor on spacecraft II. This means that the exam will appear to last for a shorter amount of time for the professor on spacecraft II.

The time interval as measured by the professor on spacecraft II can be calculated using the formula for time dilation:

t_II = t_I / sqrt(1 - v^2/c^2)

where t_I is the time interval measured by the professor on spacecraft I, v is the relative velocity between the two spacecraft, and c is the speed of light.

Assuming that the two spacecraft are moving directly away from each other, the relative velocity between them can be calculated using the formula:

v = d/t_I

where d is the distance between the two spacecraft.

Since the professor on spacecraft I stopped the exam after 88.0 minutes on her clock, we can use this as the value for t_I. The distance between the two spacecraft is not given, so we cannot calculate the relative velocity or the time interval as measured by the professor on spacecraft II.

Therefore, the answer is: Not enough information is given to calculate the time interval as measured by the professors on spacecraft II.
User Steve Lazaridis
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