InteractiveSolution 28.13 offers help in modeling this problem. A space traveler

Question

InteractiveSolution 28.13 offers help in modeling this problem.

A space traveler moving at a speed of 0.60c with respect to the earth makes a tripto a distant star that is stationary relative to the earth. Hemeasures the length of this trip to be 8.0light-years. What would be the length of this same trip (inlight-years) as measured by a traveler moving at a speed of0.85c with respect to theearth?
1 light yrs

Section 28.4 The Relativity of Length: LengthContraction
Section 28.4 The Relativity of Length: LengthContraction

Explanation / Answer

given length of the trip as observed by the space traveller L = 8.0light years relatice speed of the traveller v = 0.60c speed of light c = 3*108 m/s proper length of the trip is     L0 =L/1-v2/c2     calculating we get L0 = 10light years now new relative speed of the traveller is v ' = 0.85c length of the trip in this case is            L= L0*1-v2/c2 calculating we get 5.3 light years . calculating we get 5.3 light years .

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