# Special theory of relativity: problems and solutions

(a) A spaceship moves with speed vs = 0.80c directly towards a space station. It dispatches a food supply package (containing all the main courses) to the station with speed vr = 0.406 with respect to itself. What is the supply package's speed v'r with respect to the station? Your answer for v'r should be greater than either vr or vs; explain why this is the case.

(b) A second supply package (containing all the desserts) is mistakenly dispatched before the spaceship's cargo ejection system has fully recharged, and consequently recedes from the spaceship at a speed of only vr = 0.01c.

What is this second supply package's speed with respect to the station?

(c) If an inexperienced crew member on the space station erroneously used the Galilean velocity transformation, what results would he get for the speeds of the two supply packages? Comment on these answers in the context of

causality, and in comparison to the values you calculated in parts (a) and (b).

(d) If the ﬁrst package travels with constant speed and takes time ΔT = 5.0 days to arrive as measured by the crew member on the space station, what distance does it travel in the frame of reference of the space station? Give your answer in units of light-days, the distance travelled by light in one day.

(e) How much time elapses in transit as measured by a clock travelling with the ﬁrst supply package?

(f) Assuming that the difference in times of dispatch, and the difference in distance travelled by the two consignments is negligible, calculate the difference in arrival times at the space station between the main course and

the dessert consignments.

(g) How much less fresh than the main course will the dessert be?

(Hint: how much has each of the packages 'aged'?)

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#### Solution Summary

The problem consists of 7 different aspects of special theoty of relativity. It is well illustrated different aspects of length contraction , time dilation and different frames of reference choosen to solve a problem.