The distance from New York to Los Angeles is about 5000 km and should take about

Question

The distance from New York to Los Angeles is about 5000 km and should take about 50 h in a car driving at 100 km/h. How much shorter than 5000 km is the distance according to the car travelers? Hint: to solve the problem you must use the Taylor expansion for the factor gamma appearing in the length contraction formula, before plugging in numbers. The factor gamma is Taylor-expanded in orders of beta = upsilon/c as (1) How much less than 50 h does the trip last? Answer questions (a) and (b) if the speed of the car is 0.1c.

Explanation / Answer

the expected value of distance of the driver. D=5000*sqrt(1-v^2/c^2)=5000/(1+v^2/2c^2)=5000*(1-v^2/2c^2). so the difference.?D=5000*v^2/2c^2=2.14e-8(m). b) ?t=?D/v=7.7e-10(s). --------- so ?D=5000e3*0.1^2/2=25000(m). b) ?t=?D/v=25000/0.1c=8.3e-4(s)

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