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Special relativity

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A secret communist spacecraft is observed approaching earth at 0.500c along a straight line from mars to earth.

1.) What distance does the spacecraft observe between mars and earth if earth based measurements show a distance between those objects of 40.0 million miles?

2.) The spacecraft prepares its nuclear weapons during a 20.0 minute warm up time measured in their frame of reference. How long is earth's measurement of their warm up time?

3.) The spacecraft launches a missile towards earth at a velocity of 0.900c measured relative to their ship. What speed does an earth based measurement show for the approach of the missile?

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SOLUTION

1. As per the principles of special relativity, the distance between Mars and Earth as measured by the observer in the spacecraft will appear shorter as compared to that measured by an observer on the earth (length contraction) as per the relation :
________
L = L0√1 - v2/c2

where, L0 = length measured by the observer on earth = 40 million miles
L = length measured by the observer on the aircraft = To find
v = velocity ...

Solution Summary

This problem is a good example of application of relativistic length contraction, time dilation and velocity transformation.

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